-@inproceedings{ bender00lca,
- author = "Michael A. Bender and Martin Farach-Colton",
+@inproceedings{ bender:lca,
+ author = "Bender, M. A. and Farach-Colton, M.",
title = "The {LCA} Problem Revisited",
booktitle = "Latin American Theoretical {INformatics}",
pages = "88--94",
year = "2000",
- url = "citeseer.ist.psu.edu/bender00lca.html" }
+ url = "citeseer.ist.psu.edu/bender00lca.html"
+}
+
+@article{ frederickson:ambivalent,
+ author = "Frederickson, Greg N.",
+ title = "Ambivalent Data Structures for Dynamic 2-Edge-Connectivity and $k$ Smallest Spanning Trees",
+ journal={SIAM Journal on Computing},
+ volume={26},
+ number={2},
+ pages={484--538},
+ year={1997},
+}
-@inproceedings{ frederickson91ambivalent,
+@inproceedings{ frederickson:ambifocs,
author = "Greg N. Frederickson",
title = "Ambivalent Data Structures for Dynamic 2-Edge-Connectivity and $k$ Smallest Spanning Trees",
booktitle = "{IEEE} Symposium on Foundations of Computer Science",
pages = "632--641",
year = "1991",
- url = "citeseer.ist.psu.edu/frederickson91ambivalent.html" }
+ url = "citeseer.ist.psu.edu/frederickson91ambivalent.html"
+}
-@article{ tarjan:setunion,
+@article{ tarjan:wcsetunion,
author = {Robert E. Tarjan and Jan van Leeuwen},
title = {Worst-case Analysis of Set Union Algorithms},
- journal = {J. ACM},
+ journal = {Journal of the ACM},
volume = {31},
number = {2},
year = {1984},
issn = {0004-5411},
pages = {245--281},
doi = {http://doi.acm.org/10.1145/62.2160},
- publisher = {ACM Press},
- address = {New York, NY, USA},
+}
+
+@article{ tarjan:setunion,
+ title={{Efficiency of a Good But Not Linear Set Union Algorithm}},
+ author={Tarjan, R. E.},
+ journal={Journal of the ACM},
+ volume={22},
+ number={2},
+ pages={215--225},
+ year={1975},
}
@inproceedings { fw:transdich,
author = "M. Fredman and D. E. Willard",
title = "{Trans-dichotomous algorithms for minimum spanning trees and shortest paths}",
- booktitle = "{Proceedings of FOCS'90}",
+ booktitle={FOCS '90: Proceedings of the 31st Annual IEEE Symposium on Foundations of Computer Science},
pages = "719--725",
year = "1990"
}
@article{ boas:vebt,
author = {Peter van Emde Boas},
- title = {Preserving Order in a Forest in Less Than Logarithmic Time
- and Linear Space.},
- journal = {Inf. Process. Lett.},
+ title = {Preserving Order in a Forest in Less Than Logarithmic Time and Linear Space},
+ journal = {Information Processing Letters},
volume = {6},
number = {3},
year = {1977},
}
@article{ benamram:pm,
- author = "Ben-Amram, Amir M.",
- title = "What is a ``Pointer Machine''?",
+ author = "Ben-Amram, A. M.",
+ title = {{What is a ``Pointer Machine''?}},
journal = "SIGACTN: SIGACT News (ACM Special Interest Group on Automata and Computability Theory)",
volume = "26",
year = "1995",
@article{ chazelle:ackermann,
author = "Bernard Chazelle",
title = "{A Minimum Spanning Tree Algorithm with Inverse-Ackermann Type Complexity}",
- journal = jacm,
+ journal = "Journal of the ACM",
volume = "47",
+ number = {6},
pages = "1028--1047",
year = "2000"
}
+@inproceedings{ chazelle:almostacker,
+ title={{A faster deterministic algorithm for minimum spanning trees}},
+ author={Chazelle, Bernard},
+ booktitle={FOCS '97: Proceedings of the 38th Annual IEEE Symposium on Foundations of Computer Science},
+ pages={22},
+ year={1997},
+}
+
@article{ nesetril:history,
author = "Jaroslav Ne{\v{s}}et{\v{r}}il",
title = "{Some remarks on the history of MST-problem}",
journal = "Archivum Mathematicum",
+ publisher = "Masaryk University",
+ address = "Brno, Czech Republic",
volume = "33",
pages = "15--22",
year = "1997"
@article { boruvka:ojistem,
author = "Otakar Bor{\accent23u}vka",
title = "{O jist\'em probl\'emu minim\'aln\'\i{}m (About a Certain Minimal Problem)}",
- journal = "Pr\'ace mor. p\v{r}\'\i{}rodov\v{e}d. spol. v~Brn\v{e}",
+ journal = "Pr\'ace moravsk\'e p\v{r}\'\i{}rodov\v{e}deck\'e spole\v{c}nosti v~Brn\v{e}",
volume = "III",
year = "1926",
pages = "37--58",
- note = "Czech with German summary"
+ note = "In Czech with German summary"
}
@article { boruvka:networks,
volume = "15",
year = "1926",
pages = "153--154",
- note = "Czech"
+ note = "In Czech"
}
@article { jarnik:ojistem,
author = "Vojt\v{e}ch Jarn\'\i{}k",
title = "{O jist\'em probl\'emu minim\'aln\'\i{}m (About a Certain Minimal Problem)}",
- journal = "Pr\'ace mor. p\v{r}\'\i{}rodov\v{e}d. spol. v~Brn\v{e}",
+ journal = "Pr\'ace moravsk\'e p\v{r}\'\i{}rodov\v{e}deck\'e spole\v{c}nosti v~Brn\v{e}",
volume = "VI",
year = "1930",
pages = "57--63",
- note = "Czech"
+ note = "In Czech"
}
@book { tarjan:dsna,
author = "Robert E. Tarjan",
title = "{Data structures and network algorithms}",
- series = "{CMBS-NSF Regional Conf. Series in Appl. Math.}",
+ series = "{CMBS-NSF Regional Conference Series in Applied Mathematics}",
volume = 44,
year = "1983",
- publisher = "SIAM"
-}
-
-@article { gh:history,
- author = "R. L. Graham and P. Hell",
- title = "{On the history of the minimum spanning tree problem}",
- journal = "{Annals of the History of Computing}",
- volume = "7",
- year = "1985",
- pages = "43--57"
+ publisher = "Society for Industrial and Applied Mathematics"
}
@techreport { pettie:ackermann,
author = "Seth Pettie",
- title = "{Finding minimum spanning trees in $\O(m\alpha(m,n))$ time}",
- institution = "Univ. of Texas at Austin",
+ title = "{Finding minimum spanning trees in $\O(m\timesalpha(m,n))$ time}",
+ institution = "University of Texas at Austin",
year = "1999",
number = "TR99-23",
type = "Tech Report"
}
-@inproceedings { pettie:optimal,
+@article{ pettie:optimal,
+ author = {Seth Pettie and Vijaya Ramachandran},
+ title= {An optimal minimum spanning tree algorithm},
+ journal = {Journal of the ACM},
+ volume = {49},
+ number = {1},
+ year = {2002},
+ pages = {16--34},
+}
+
+@inproceedings { pettie:optimal-conf,
author = "Seth Pettie and Vijaya Ramachandran",
title = "{An Optimal Minimum Spanning Tree Algorithm}",
- booktitle = "{Proceedings of ICALP'2000}",
+ booktitle = "{Proceedings of ICALP 2000}",
year = "2000",
- publisher = "Springer Verlag",
pages = "49--60"
}
@article { karger:randomized,
author = "D. R. Karger and P. N. Klein and R. E. Tarjan",
- title = "{Linear expected-time algorithms for connectivity problems}",
- journal = jacm,
+ title = "{A Randomized Linear-Time Algorithm to Find Minimum Spanning Trees}",
+ journal = "Journal of the ACM",
volume = "42",
+ number = "2",
pages = "321--328",
year = "1995"
}
+@inproceedings { karger:sampling,
+ title={Random sampling in matroids, with applications to graph connectivity and minimum spanning trees},
+ author={Karger, D. R.},
+ booktitle={FOCS '93: Proceedings of the 34th Annual IEEE Symposium on Foundations of Computer Science},
+ year={1993},
+ pages={84--93}
+}
+
+@article{ chan:backward,
+ title={{Backwards analysis of the Karger-Klein-Tarjan algorithm for minimum spanning trees}},
+ author={Chan, T. M.},
+ journal={Information Processing Letters},
+ volume={67},
+ number={6},
+ pages={303--304},
+ year={1998},
+}
+
@article { frederickson:online,
author = "Greg N. Frederickson",
title = "{Data structures for on-line updating of minimum spanning trees}",
author = "Martin Mare\v{s}",
title = "{Two linear time algorithms for MST on minor closed graph classes}",
journal = "{Archivum Mathematicum}",
+ publisher = "Masaryk University",
+ address = "Brno, Czech Republic",
volume = "40",
pages = "315--320",
year = "2004"
booktitle = "Algorithms --- ESA 2007: 15th Annual European Symposium",
location = "Eilat, Israel, October 8--10, 2007",
volume = "4698",
- series = "Lecture Notes in Computer Science",
+ series = {{Lecture Notes in Computer Science}},
pages = "187--193",
- publisher = "Springer",
+ publisher = "Springer Verlag",
year = "2007",
}
@article{ ft:fibonacci,
author = {Michael L. Fredman and Robert Endre Tarjan},
title = {Fibonacci heaps and their uses in improved network optimization algorithms},
- journal = {J. ACM},
+ journal = {Journal of the ACM},
volume = {34},
number = {3},
year = {1987},
issn = {0004-5411},
pages = {596--615},
doi = {http://doi.acm.org/10.1145/28869.28874},
- publisher = {ACM Press},
- address = {New York, NY, USA},
}
@article{ komlos:verify,
@inproceedings{ king:verify,
author = "Valerie King",
title = "A Simpler Minimum Spanning Tree Verification Algorithm",
- booktitle = "Workshop on Algorithms and Data Structures",
+ booktitle = "{Algorithms and Data Structures --- WADS '95: 4th International Workshop}",
pages = "440--448",
year = "1995",
- url = "citeseer.ist.psu.edu/king95simpler.html" }
+ location = "Kingston, Canada",
+ volume = "955",
+ series = "Lecture Notes in Computer Science",
+ publisher = "Springer Verlag",
+ url = "citeseer.ist.psu.edu/king95simpler.html"
+}
@article{ king:verifytwo,
title={{A Simpler Minimum Spanning Tree Verification Algorithm}},
@inproceedings{ thorup:aczero,
author = {Mikkel Thorup},
title = {{On ${\rm AC}^0$ Implementations of Fusion Trees and Atomic Heaps}},
- booktitle = {SODA '03: Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms},
+ booktitle = {SODA 2003: Proceedings of the 14th annual ACM-SIAM Symposium on Discrete algorithms},
year = {2003},
isbn = {0-89871-538-5},
pages = {699--707},
location = {Baltimore, Maryland},
- publisher = {Society for Industrial and Applied Mathematics},
- address = {Philadelphia, PA, USA},
}
@article{ kruskal:mst,
title={{On the Shortest Spanning Subtree of a Graph and the Traveling Salesman Problem}},
- author={Kruskal Jr, J.B.},
+ author={Kruskal, Jr, J. B.},
journal={Proceedings of the American Mathematical Society},
volume={7},
number={1},
pages={48--50},
year={1956},
- publisher={JSTOR}
}
@book{ diestel:gt,
title={{Graph Theory}},
author={Diestel, R.},
year={2005},
- publisher={Springer-Verlag Berlin and Heidelberg GmbH \& Co.}
-}
-
-@article{ thorup:pq,
- title={{Integer priority queues with decrease key in constant time and the single source shortest paths problem}},
- author={Thorup, M.},
- journal={Proceedings of the thirty-fifth ACM Symposium on Theory of Computing},
- pages={149--158},
- year={2003},
- publisher={ACM Press New York, NY, USA}
+ publisher={Springer Verlag}
}
@article{ graham:msthistory,
title={{On the history of the minimum spanning tree problem}},
- author={Graham, R.L. and Hell, P.},
+ author={Graham, R. L. and Hell, P.},
journal={Annals of the History of Computing},
volume={7},
number={1},
@article{ cayley:trees,
title={{A theorem on trees}},
author={Cayley, Arthur},
- journal={Quart. J. Math},
+ journal={Quarterly Journal of Mathematics},
volume={23},
year={1889},
pages={376--378}
number={1},
pages={269--271},
year={1959},
- publisher={Springer}
+ publisher={Springer Verlag}
}
@article{ prim:mst,
volume={206},
pages={310},
year={1938},
- note={French}
+ note={In French}
}
@incollection { sollin:mst,
editor={Berge, C. and Ghouilla-Houri, A.},
publisher={Wiley, New York},
year={1965},
- note={French}
+ note={In French}
}
@article{ boyer:cutting,
title={{On the cutting edge: Simplified $\O(n)$ planarity by edge addition}},
- author={Boyer, J.M. and Myrvold, W.J.},
+ author={Boyer, J. M. and Myrvold, W. J.},
journal={Journal of Graph Algorithms and Applications},
volume={8},
number={3},
@inproceedings{ takaoka:twothree,
title={{Theory of 2-3 Heaps}},
author={Takaoka, T. and Christchurch, N. Z.},
- booktitle={Computing and Combinatorics: 5th Annual International Conference, COCOON'99},
+ booktitle={Computing and Combinatorics: 5th Annual International Conference, COCOON '99},
location={Tokyo, Japan},
year={1999},
pages={41--50},
- publisher={Springer},
+ publisher={Springer Verlag},
series={{Lecture Notes in Computer Science}},
volume={1627}
}
location={Sydney, Australia},
year={2000},
pages={362--372},
- publisher={Springer},
+ publisher={Springer Verlag},
series={{Lecture Notes in Computer Science}},
volume={1858}
}
@book{ clrs,
title={{Introduction to Algorithms}},
- author={Leiserson, C.E. and Rivest, R.L. and Cormen, T.H. and Stein, C.},
+ author={Leiserson, C. E. and Rivest, R. L. and Cormen, T. H. and Stein, C.},
year={2001},
publisher={McGraw-Hill}
}
-@inproceedings{ pettie:onlineverify,
+@article{ pettie:onlineverify,
+ author = {Seth Pettie},
+ title = {An Inverse-{A}ckermann Type Lower Bound for Online
+ Minimum Spanning Tree Verification},
+ journal = {Combinatorica},
+ volume = {26},
+ number = {2},
+ pages = {207--230},
+ year = {2006},
+}
+
+@inproceedings{ pettie:onlineverify-conf,
author = "S. Pettie",
title = "An inverse-{A}ckermann style lower bound for the online minimum spanning
tree verification problem",
- booktitle = "Proc. 43rd Annual Symp. on the Foundations of Computer Science, Vancouver, Canada",
+ booktitle = "FOCS 2002: Proceedings of the 43rd Annual IEEE Symposium on Foundations of Computer Science",
year = "2002",
url = "citeseer.ist.psu.edu/article/pettie02inverseackermann.html"
}
@article{ dixon:verify,
author = "Brandon Dixon and Monika Rauch and Robert Endre Tarjan",
title = "Verification and Sensitivity Analysis of Minimum Spanning Trees in Linear Time",
- journal = "SIAM J. Comput.",
+ journal = "SIAM Journal of Computing",
volume = "21",
number = "6",
pages = "1184-1192",
url = "citeseer.ist.psu.edu/dixon92verification.html"
}
-inproceedings{ pettie:minirand,
+@inproceedings{ pettie:minirand,
author = {Seth Pettie and Vijaya Ramachandran},
title = {Minimizing randomness in minimum spanning tree, parallel connectivity, and set maxima algorithms},
- booktitle = {SODA '02: Proceedings of the thirteenth annual ACM-SIAM Symposium on Discrete Algorithms},
+ booktitle = {SODA 2002: Proceedings of the 13th annual ACM-SIAM Symposium on Discrete Algorithms},
year = {2002},
isbn = {0-89871-513-X},
pages = {713--722},
location = {San Francisco, California},
- publisher = {Society for Industrial and Applied Mathematics},
- address = {Philadelphia, PA, USA}
}
-@article{ buchsbaum:verify,
+@inproceedings{ buchsbaum:verify,
title={{Linear-time pointer-machine algorithms for least common ancestors, MST verification, and dominators}},
- author={Buchsbaum, A.L. and Kaplan, H. and Rogers, A. and Westbrook, J.R.},
- journal={Proceedings of the thirtieth annual ACM Symposium on Theory of Computing},
+ author={Buchsbaum, A. L. and Kaplan, H. and Rogers, A. and Westbrook, J. R.},
+ booktitle={STOC 1998: Proceedings of the 30th annual ACM Symposium on Theory of Computing},
pages={279--288},
year={1998},
- publisher={ACM Press New York, NY, USA}
}
@article{ bacala:parametric,
number={1},
pages={57--74},
year={1997},
- publisher={Elsevier}
}
@inproceedings{ katriel:cycle,
author = "I. Katriel and P. Sanders and J. Tr{\"a}ff",
title = "A practical minimum spanning tree algorithm using the cycle property",
- booktitle = "11th European Symposium on Algorithms (ESA)",
- number = "2832",
- series = "LNCS",
+ booktitle = "Algorithms --- ESA 2003: 11th European Symposium",
+ volume = "2832",
+ series = "Lecture Notes in Computer Science",
pages = "679--690",
- publisher = "Springer",
+ publisher = "Springer Verlag",
year = "2003",
url = "citeseer.ist.psu.edu/katriel03practical.html"
}
@article{ alstrup:nca,
- title={{Nearest common ancestors: a survey and a new distributed algorithm}},
+ title={{Nearest Common Ancestors: A Survey and a new Distributed Algorithm}},
author={Alstrup, S. and Gavoille, C. and Kaplan, H. and Rauhe, T.},
- journal={Proceedings of the fourteenth annual ACM symposium on Parallel algorithms and architectures},
+ journal={Proceedings of the 14th annual ACM Symposium on Parallel algorithms and architectures},
pages={258--264},
year={2002},
- publisher={ACM Press New York, NY, USA}
}
@article{ gabow:mst,
title={{Efficient algorithms for finding minimum spanning trees in undirected and directed graphs}},
- author={Gabow, H.N. and Galil, Z. and Spencer, T. and Tarjan, R.E.},
+ author={Gabow, H. N. and Galil, Z. and Spencer, T. and Tarjan, R. E.},
journal={Combinatorica},
volume={6},
number={2},
pages={109--122},
year={1986},
- publisher={Springer}
}
-@Unpublished{ eisner:tutorial,
+@online{ eisner:tutorial,
author = {Jason Eisner},
- title = {State-of-the-Art Algorithms for Minimum Spanning
- Trees: A Tutorial Discussion},
- note = {Manuscript available online (78 pages), University of Pennsylvania},
+ title = {{State-of-the-Art Algorithms for Minimum Spanning
+ Trees: A~Tutorial Discussion}},
+ note = {Manuscript available online (78 pages), University of Pennsylvania},
year = 1997,
- url = {http://cs.jhu.edu/~jason/papers/#ms97},
+ url = {http://cs.jhu.edu/{\char126}jason/papers/\#ms97},
}
@article{ aho:lca,
year = {1997},
isbn = {0-201-89683-4},
publisher = {Addison Wesley Longman Publishing Co., Inc.},
- address = {Redwood City, CA, USA},
}
@book{ knuth:seminalg,
year = {1997},
isbn = {978-0-201-89684-8},
publisher = {Addison Wesley Longman Publishing Co., Inc.},
- address = {Redwood City, CA, USA},
}
@book{ knuth:sas,
year = {1998},
isbn = {978-0-201-89685-5},
publisher = {Addison Wesley Longman Publishing Co., Inc.},
- address = {Redwood City, CA, USA},
}
@inproceedings{ hagerup:wordram,
author = {Torben Hagerup},
title = {{Sorting and Searching on the Word RAM}},
- booktitle = {STACS '98: Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science},
+ booktitle = {STACS '98: Proceedings of the 15th annual Symposium on Theoretical Aspects of Computer Science},
year = {1998},
isbn = {3-540-64230-7},
pages = {366--398},
- publisher = {Springer-Verlag},
- address = {London, UK},
}
@inproceedings{ cook:ram,
pages = {73--80},
location = {Denver, Colorado, United States},
doi = {http://doi.acm.org/10.1145/800152.804898},
- publisher = {ACM},
- address = {New York, NY, USA},
}
@book{ okasaki:funcds,
@article{ hagerup:dd,
title={{Deterministic Dictionaries}},
- author={Hagerup, T. and Miltersen, P.B. and Pagh, R.},
- journal={J. Algorithms},
+ author={Hagerup, T. and Miltersen, P. B. and Pagh, R.},
+ journal={Journal of Algorithms},
volume={41},
number={1},
pages={69--85},
@article{ fredman:sst,
title={{Storing a Sparse Table with $\O(1)$ Worst Case Access Time}},
- author={Fredman, M.L. and Koml{\'o}s, J. and Szemer{\'e}di, E.},
- journal={Journal of the ACM (JACM)},
+ author={Fredman, M. L. and Koml{\'o}s, J. and Szemer{\'e}di, E.},
+ journal={Journal of the ACM},
volume={31},
number={3},
pages={538--544},
year={1984},
- publisher={ACM Press New York, NY, USA}
}
@book{ motwani:randalg,
@article{ fw:fusion,
title={{Surpassing the information theoretic bound with fusion trees}},
- author={Fredman, M.L. and Willard, D.E.},
+ author={Fredman, M. L. and Willard, D. E.},
journal={Journal of Computer and System Sciences},
volume={47},
number={3},
pages={424--436},
year={1993},
- publisher={Academic Press, Inc. Orlando, FL, USA}
}
-@article{ han:detsort,
+@inproceedings{ han:detsort,
title={{Deterministic sorting in $\O(n \log\log n)$ time and linear space}},
author={Han, Y.},
- journal={Proceedings of the thiry-fourth annual ACM Symposium on Theory of Computing},
+ booktitle={STOC 2002: Proceedings of the 34th annual ACM Symposium on Theory of Computing},
pages={602--608},
year={2002},
- publisher={ACM Press New York, NY, USA}
}
-@article{ hanthor:randsort,
+@inproceedings{ hanthor:randsort,
title={{Integer Sorting in $\O(n\sqrt{\log\log n})$ Expected Time and Linear Space}},
author={Han, Y. and Thorup, M.},
- journal={Proceedings of the 43rd Symposium on Foundations of Computer Science},
+ booktitle={FOCS 2002: Proceedings of the 43rd Annual IEEE Symposium on Foundations of Computer Science},
pages={135--144},
year={2002},
- publisher={IEEE Computer Society Washington, DC, USA}
}
-@article{ ito:newrap,
+@inproceedings{ ito:newrap,
title={{Efficient Initial Approximation and Fast Converging Methods for Division and Square Root}},
author={Ito, M. and Takagi, N. and Yajima, S.},
- journal={Proc. 12th IEEE Symp. Computer Arithmetic},
+ booktitle={Proceedings of the 12th IEEE Symposium on Computer Arithmetic},
pages={2--9},
year={1995}
}
-@article{ brodnik:lsb,
+@inproceedings{ brodnik:lsb,
title={{Computation of the least significant set bit}},
author={Brodnik, A.},
- journal={Proceedings of the 2nd Electrotechnical and Computer Science Conference, Portoroz, Slovenia},
+ booktitle={Proceedings of the 2nd Electrotechnical and Computer Science Conference, Portoroz, Slovenia},
year={1993}
}
number={4},
pages={265--268},
year={1967},
- publisher={Springer},
- note={German}
+ publisher={Springer Verlag},
+ note={In German}
}
@inproceedings{ gustedt:parallel,
author = "Jens Gustedt",
title = "Minimum Spanning Trees for Minor-Closed Graph Classes in Parallel",
- booktitle = "Symposium on Theoretical Aspects of Computer Science",
+ booktitle = "STACS '98: Proceedings of the 15th annual Symposium on Theoretical Aspects of Computer Science",
pages = "421-431",
year = "1998",
url = "citeseer.ist.psu.edu/223918.html"
@article{ myrvold:rank,
title={{Ranking and unranking permutations in linear time}},
- author={Myrvold, W.J. and Ruskey, F.},
+ author={Myrvold, W. J. and Ruskey, F.},
journal={Information Processing Letters},
volume={79},
number={6},
@article{ ruskey:ham,
title={{The Hamiltonicity of directed-Cayley graphs (or: A tale of backtracking)}},
author={Ruskey, F. and Jiang, M. and Weston, A.},
- journal={Discrete Appl. Math},
+ journal={Discrete Applied Mathematics},
volume={57},
pages={75--83},
year={1995}
}
@article{ ruskey:hce,
- title={{Hamilton Cycles that Extend Transposition Matchings in Cayley Graphs of Sn}},
- author={Ruskey, F. and Savage, C.D.},
+ title={{Hamilton Cycles that Extend Transposition Matchings in Cayley Graphs of $S_n$}},
+ author={Ruskey, F. and Savage, C. D.},
journal={SIAM Journal on Discrete Mathematics},
volume={6},
number={1},
@book{ reingold:catp,
title={{Combinatorial Algorithms: Theory and Practice}},
- author={Reingold, E.M.},
+ author={Reingold, E. M.},
year={1977},
- publisher={Prentice Hall College Div}
+ publisher={Prentice Hall College Div.}
}
@inproceedings{ dietz:oal,
year = {1989},
isbn = {3-540-51542-9},
pages = {39--46},
- publisher = {Springer-Verlag},
- address = {London, UK},
}
@book { ss:fifteen,
number={2},
pages={325--357},
year={2004},
- publisher={Academic Press, Inc. Orlando, FL, USA}
}
@book{ matnes:idm,
publisher={Oxford University Press}
}
-@article{ stanley:econe,
- title={{Enumerative combinatorics. Vol. 1}},
- author={Stanley, R.P.},
- journal={Cambridge Studies in Advanced Mathematics},
- volume={49},
- year={1997}
+@book{ stanley:econe,
+ title={{Enumerative Combinatorics. Vol. 1 (2nd ed.)}},
+ author={Stanley, R. P.},
+ publisher={Cambridge University Press},
+ year={2000}
}
@article{ kaplansky:rooks,
title={{The problem of the rooks and its applications}},
author={Kaplansky, I. and Riordan, J.},
- journal={Duke Math. J},
+ journal={Duke Mathematical Journal},
volume={13},
number={2},
pages={259--268},
- year={1946}
+ year={1946},
+ publisher={Duke University Press}
}
@article{ dinic:flow,
@article{ even:dinic,
author = {Shimon Even and Robert Endre Tarjan},
title = {Network Flow and Testing Graph Connectivity},
- publisher = {SIAM},
year = {1975},
journal = {SIAM Journal on Computing},
volume = {4},
year={2004}
}
-@article{ kasteleyn:crystals,
+/* HACK: bibtex cannot handle a part of a book with its own name */
+@inproceedings{ kasteleyn:crystals,
title={{Graph theory and crystal physics}},
author={Kasteleyn, P. W.},
- journal={Graph Theory and Theoretical Physics},
+ booktitle={Graph Theory and Theoretical Physics},
publisher={Academic Press, London},
pages={43--110},
year={1967}
}
-@article{ yuster:matching,
+@inproceedings{ yuster:matching,
title={{Maximum matching in graphs with an excluded minor}},
author={Yuster, R. and Zwick, U.},
- journal={Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms},
+ booktitle={SODA 2007: Proceedings of the 18th annual ACM-SIAM Symposium on Discrete Algorithms},
pages={108--117},
year={2007},
- publisher={Society for Industrial and Applied Mathematics Philadelphia, PA, USA}
}
@article{ mucha:matching,
number={1},
pages={3--20},
year={2006},
- publisher={Springer}
}
@article {lovasz:minors,
}
@article{ andersson:fusion,
- title={{Fusion trees can be implemented with AC0 instructions only}},
- author={Andersson, A. and Miltersen, P.B. and Thorup, M.},
+ title={{Fusion trees can be implemented with AC$^0$ instructions only}},
+ author={Andersson, A. and Miltersen, P. B. and Thorup, M.},
journal={Theoretical Computer Science},
volume={215},
number={1-2},
pages={337--344},
year={1999},
- publisher={Elsevier}
+}
+
+@article{ thorup:rampq,
+ title={{On RAM priority queues}},
+ author={THORUP, M.},
+ journal={SIAM Journal on Computing},
+ volume={30},
+ number={1},
+ pages={86--109},
+ year={2001},
+}
+
+@article{ thorup:pqsssp,
+ title={{Integer priority queues with decrease key in constant time and the single source shortest paths problem}},
+ author={Thorup, M.},
+ journal={STOC 2003: Proceedings of the 35th ACM Symposium on Theory of Computing},
+ pages={149--158},
+ year={2003},
+}
+
+@article{ chazelle:mstapprox,
+ title={{Approximating the Minimum Spanning Tree Weight in Sublinear Time}},
+ author={Chazelle, B. and Rubinfeld, R. and Trevisan, L.},
+ journal={SIAM Journal on Computing},
+ volume={34},
+ pages={1370},
+ year={2005},
+}
+
+@inproceedings{ czumaj:metric,
+ author = {Artur Czumaj and Christian Sohler},
+ title = {Estimating the weight of metric minimum spanning trees in sublinear-time},
+ booktitle = {STOC 2004: Proceedings of the 36th annual ACM Symposium on Theory of Computing},
+ year = {2004},
+ isbn = {1-58113-852-0},
+ pages = {175--183},
+ location = {Chicago, IL, USA},
+}
+
+@inproceedings{ czumaj:euclidean,
+ author = {Artur Czumaj and Funda Erg\"{u}n and Lance Fortnow and Avner Magen and Ilan Newman and Ronitt Rubinfeld and Christian Sohler},
+ title = {{Sublinear-time approximation of Euclidean minimum spanning tree}},
+ booktitle = {SODA 2003: Proceedings of the 14th annual ACM-SIAM Symposium on Discrete Algorithms},
+ year = {2003},
+ isbn = {0-89871-538-5},
+ pages = {813--822},
+}
+
+@book{ ieee:binfp,
+ author = {IEEE},
+ title = {IEEE Standard 754-1985 for Binary Floating-point Arithmetic},
+ year = {1985},
+ publisher = {IEEE}
+}
+
+@article{ dgoldberg:fp,
+ title={{What every computer scientist should know about floating-point arithmetic}},
+ author={Goldberg, D.},
+ journal={ACM Computing Surveys},
+ volume={23},
+ number={1},
+ pages={5--48},
+ year={1991},
+}
+
+@article{ thorup:floatint,
+ title={{Floats, Integers, and Single Source Shortest Paths}},
+ author={Thorup, M.},
+ journal={Journal of Algorithms},
+ volume={35},
+ number={2},
+ pages={189--201},
+ year={2000},
+}
+
+@article{ shamos:closest,
+ title={{Closest-point problems}},
+ author={Shamos, M. I. and Hoey, D.},
+ journal={FOCS '75: Proceedings of the 16th Annual IEEE Symposium on Foundations of Computer Science},
+ pages={151--162},
+ year={1975}
+}
+
+@article{ fortune:voronoi,
+ title={{A sweepline algorithm for Voronoi diagrams}},
+ author={Fortune, S.},
+ journal={Algorithmica},
+ volume={2},
+ number={1},
+ pages={153--174},
+ year={1987},
+}
+
+@article{ zhou:nodel,
+ title={{Efficient minimum spanning tree construction without Delaunay triangulation}},
+ author={Zhou, H. and Shenoy, N. and Nicholls, W.},
+ journal={Information Processing Letters},
+ volume={81},
+ number={5},
+ pages={271--276},
+ year={2002},
+}
+
+@techreport{ eppstein:spanning,
+ title={{Spanning Trees and Spanners}},
+ author={Eppstein, D.},
+ year={1996},
+ institution={Information and Computer Science, University of California, Irvine},
+ number = {96-16},
+}
+
+@article{ garey:steiner,
+ title={{The Complexity of Computing Steiner Minimal Trees}},
+ author={Garey, M. R. and Graham, R. L. and Johnson, D. S.},
+ journal={SIAM Journal on Applied Mathematics},
+ volume={32},
+ number={4},
+ pages={835--859},
+ year={1977},
+}
+
+@article{ garey:rectisteiner,
+ title={{The Rectilinear Steiner Tree Problem is NP-Complete}},
+ author={Garey, M. R. and Johnson, D. S.},
+ journal={SIAM Journal on Applied Mathematics},
+ volume={32},
+ number={4},
+ pages={826--834},
+ year={1977},
+}
+
+@article{ proemel:steiner,
+ title={{A new approximation algorithm for the Steiner tree problem with performance ratio $5/3$}},
+ author={Promel, H. J. and Steger, A.},
+ journal={Journal of Algorithms},
+ volume={36},
+ pages={89--101},
+ year={2000}
+}
+
+@article{ arora:tspapx,
+ title={{Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems}},
+ author={Arora, S.},
+ journal={Journal of the ACM},
+ volume={45},
+ number={5},
+ pages={753--782},
+ year={1998},
+}
+
+@article{ harel:nca,
+ title={{Fast algorithms for finding nearest common ancestors}},
+ author={Harel, D. and Tarjan, R. E.},
+ journal={SIAM Journal on Computing},
+ volume={13},
+ number={2},
+ pages={338--355},
+ year={1984},
+}
+
+@article{ gomoryhu,
+ author = "R. E. Gomory and T. C. Hu",
+ title = "Multi-Terminal Network Flows",
+ journal = "{Journal of SIAM}",
+ volume = {9},
+ number = {4},
+ year = {1961},
+ pages = {551--570}
+}
+
+@inproceedings{ bhalgat:ght,
+ author = {Ramesh Hariharan and Telikepalli Kavitha and Debmalya Panigrahi and Anand Bhalgat},
+ title = {{An $\widetilde\O(mn)$ Gomory-Hu tree construction algorithm for unweighted graphs}},
+ booktitle = {STOC 2007: Proceedings of the 39th annual ACM Symposium on Theory of Computing},
+ year = {2007},
+ isbn = {978-1-59593-631-8},
+ pages = {605--614},
+ location = {San Diego, California, USA},
+ doi = {http://doi.acm.org/10.1145/1250790.1250879},
+}
+
+@article{ sleator:trees,
+ title={{A data structure for dynamic trees}},
+ author={Sleator, D. D. and Tarjan, R. E.},
+ journal={Journal of Computer and System Sciences},
+ volume={26},
+ number={3},
+ pages={362--391},
+ year={1983},
+}
+
+@article{ chernoff,
+ title={{A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations}},
+ author={Chernoff, H.},
+ journal={The Annals of Mathematical Statistics},
+ volume={23},
+ number={4},
+ pages={493--507},
+ year={1952},
+ publisher={JSTOR}
+}
+
+@article{ pettie:parallel,
+ author = {Seth Pettie and Vijaya Ramachandran},
+ title = {A randomized time-work optimal parallel algorithm for
+ finding a minimum spanning forest},
+ journal = {SIAM Journal of Computing},
+ volume = {31},
+ number = {6},
+ year = {2002},
+ pages = {1879--1895},
+}
+
+@article{ chazelle:softheap,
+ author = {Bernard Chazelle},
+ title = {The soft heap: an approximate priority queue with optimal error rate},
+ journal = {Journal of the ACM},
+ volume = {47},
+ number = {6},
+ year = {2000},
+ issn = {0004-5411},
+ pages = {1012--1027},
+ doi = {http://doi.acm.org/10.1145/355541.355554},
+}
+
+@article{ propp:randommst,
+ author = {James Gary Propp and David Bruce Wilson},
+ title = {How to get a perfectly random sample from a generic Markov chain and generate a random spanning tree of a directed graph},
+ journal = {Journal of Algorithms},
+ volume = {27},
+ number = {2},
+ year = {1998},
+ issn = {0196-6774},
+ pages = {170--217},
+ doi = {http://dx.doi.org/10.1006/jagm.1997.0917},
+}
+
+@article{ vuillemin:binheap,
+ title={{A Data Structure for Manipulating Priority Queues}},
+ author={Vuillemin, Jean},
+ journal={Communications of the ACM},
+ volume = 21,
+ number = 4,
+ pages={309--315},
+ year={1978}
+}
+
+@article{ hoare:qsort,
+ title={{Quicksort}},
+ author={Hoare, Charles Anthony Richard},
+ journal={The Computer Journal},
+ volume={5},
+ number={1},
+ pages={10--16},
+ year={1962},
+ publisher={British Computer Society}
+}
+
+@article{ blum:selection,
+ title={{Time bounds for selection}},
+ author={Blum, M. and Floyd, R. W. and Pratt, V. and Rivest, R. L. and Tarjan, R. E.},
+ journal={Journal of Computer and System Sciences},
+ volume={7},
+ number={4},
+ pages={448--461},
+ year={1973}
+}
+
+@article{ hoare:qselect,
+ author = {Hoare, Charles Anthony Richard},
+ title = {Algorithm 65: find},
+ journal = {Communications of the ACM},
+ volume = {4},
+ number = {7},
+ year = {1961},
+ issn = {0001-0782},
+ pages = {321--322},
+ doi = {http://doi.acm.org/10.1145/366622.366647},
+}
+
+@article{ dinitz:treeiso,
+ title={{On an algorithm of Zemlyachenko for subtree isomorphism}},
+ author={Dinitz, Y. and Itai, A. and Rodeh, M.},
+ journal={Information Processing Letters},
+ volume={70},
+ number={3},
+ pages={141--146},
+ year={1999},
+}
+
+@inproceedings{ zemlay:treeiso,
+ title={{Determining tree isomorphism}},
+ author={Zemlayachenko, V. N.},
+ booktitle={{Voprosy Kibernetiki, Proceedings of the Seminar on Combinatorial Mathematics}},
+ location={Moscow 1971},
+ publisher={{Scientific Council of the Complex Problem ``Kibernetika'', Akad. Nauk SSSR}},
+ year={1973},
+ pages={54--60},
+ note={In Russian},
+}
+
+@inproceedings{ alstrup:marked,
+ title={{Marked ancestor problems}},
+ author={Alstrup, S. and Husfeldt, T. and Rauhe, T.},
+ booktitle={FOCS '98: Proceedings of the 39th Annual IEEE Symposium on Foundations of Computer Science},
+ pages={534--543},
+ year={1998}
+}
+
+@inproceedings{ arvind:isomorph,
+ title={{Graph isomorphism is in SPP}},
+ author={Arvind, V. and Kurur, P. P.},
+ booktitle={FOCS 2002: Proceedings of the 43rd Annual IEEE Symposium on Foundations of Computer Science},
+ pages={743--750},
+ year={2002}
+}
+
+@article{ ackermann:function,
+ title={{Zum Hilbertschen Aufbau der reellen Zahlen}},
+ author={Ackermann, W.},
+ journal={Mathematische Annalen},
+ volume={99},
+ number={1},
+ pages={118--133},
+ year={1928},
+ publisher={Springer Verlag},
+ notes={In German}
+}
+
+@article{ klazar:gdss,
+ title={{Generalized Davenport--Schinzel Sequences: Results, problems, and applications}},
+ author={Klazar, M.},
+ journal={INTEGERS: The Electronic Journal of Combinatorial Number Theory},
+ volume={2},
+ number={A11},
+ year={2002}
+}
+
+@inproceedings{ fredman:cellprobe,
+ author = {M. Fredman and M. Saks},
+ title = {The cell probe complexity of dynamic data structures},
+ booktitle = {STOC '89: Proceedings of the 21st annual ACM Symposium on Theory of Computing},
+ year = {1989},
+ isbn = {0-89791-307-8},
+ pages = {345--354},
+ location = {Seattle, Washington, United States},
+ doi = {http://doi.acm.org/10.1145/73007.73040},
+}
+
+@article{ henzinger:randdyn,
+ title={{Randomized Fully Dynamic Graph Algorithms with Polylogarithmic Time per Operation}},
+ author={Henzinger, M. R. and King, V.},
+ journal={Journal of the ACM},
+ volume={46},
+ number={4},
+ pages={502--516},
+ year={1999}
+}
+
+@article{ holm:polylog,
+ title={{Poly-logarithmic deterministic fully-dynamic algorithms for connectivity, minimum spanning tree, 2-edge, and biconnectivity}},
+ author={Holm, J. and de Lichtenberg, K. and Thorup, M.},
+ journal={Journal of the ACM},
+ volume={48},
+ number={4},
+ pages={723--760},
+ year={2001},
+}
+
+@article{ frederickson:dynamic,
+ title={{Data structures for on-line updating of minimum spanning trees, with applications}},
+ author={Frederickson, G. N.},
+ journal={SIAM Journal of Computing},
+ volume={14},
+ pages={781--798},
+ year={1985}
+}
+
+@article{ eppstein:sparsify,
+ title={{Sparsification --- a technique for speeding up dynamic graph algorithms}},
+ author={Eppstein, D. and Galil, Z. and Italiano, G. F. and Nissenzweig, A.},
+ journal={Journal of the ACM},
+ volume={44},
+ number={5},
+ pages={669--696},
+ year={1997},
+}
+
+@inproceedings{ henzinger:mst,
+ title={{Maintaining minimum spanning trees in dynamic graphs}},
+ author={Henzinger, M. R. and King, V.},
+ booktitle={ICALP '97: Proceedings of the 24th International Colloquium on Automata, Languages and Programming},
+ pages={594--604},
+ year={1997},
+}
+
+@mastersthesis { mares:dga,
+ title={{Dynamick\'e grafov\'e algoritmy (Dynamic Graph Algorithms)}},
+ author={Martin Mare\v{s}},
+ school={Charles University in Prague, Faculty of Math and Physics},
+ year={2000},
+ note={In Czech}
+}
+
+@techreport{ henzinger:twoec,
+ title = {Fully dynamic 2-edge-connectivity algorithm in polylogarithmic time per operation},
+ author = {Monika Rauch Henzinger and Valerie King},
+ type = {Technical note},
+ institution = {Digital Equipment Corp., Systems Research Center},
+ number = {1997-004},
+ year = {1997},
+ url = {http://gatekeeper.dec.com/pub/DEC/SRC/technical-notes/abstracts/src-tn-1997-004.html}
+}
+
+@book{ overmars:ds,
+ author = {Mark H. Overmars},
+ title = {Design of Dynamic Data Structures},
+ year = {1987},
+ isbn = {038712330X},
+ publisher = {Springer Verlag},
+ series={{Lecture Notes in Computer Science}},
+ volume={156}
+}
+
+@article{ eppstein:ksmallest,
+ title={{Finding the $k$~Smallest Spanning Trees}},
+ author={Eppstein, D.},
+ journal={BIT},
+ volume={32},
+ number={2},
+ pages={237--248},
+ year={1992},
+ publisher={Springer Verlag}
+}
+
+@article{ katoh:ksmallest,
+ title={{An Algorithm for Finding\$ K\$ Minimum Spanning Trees}},
+ author={Katoh, N. and Ibaraki, T. and Mine, H.},
+ journal={SIAM Journal on Computing},
+ volume={10},
+ pages={247},
+ year={1981},
+}
+
+@inproceedings{ thorup:nearopt,
+ author = {Mikkel Thorup},
+ title = {Near-optimal fully-dynamic graph connectivity},
+ booktitle = {STOC 2000: Proceedings of the 32nd annual ACM Symposium on Theory of Computing},
+ year = {2000},
+ isbn = {1-58113-184-4},
+ pages = {343--350},
+ location = {Portland, Oregon, United States},
+ doi = {http://doi.acm.org/10.1145/335305.335345},
+}
+
+@article{ henzinger:lowerbounds,
+ title={{Lower Bounds for Fully Dynamic Connectivity Problems in Graphs}},
+ author={Henzinger, M. R. and Fredman, M. L.},
+ journal={Algorithmica},
+ volume={22},
+ number={3},
+ pages={351--362},
+ year={1998},
+}
+
+@article{ thorup:usssp,
+ title={{Undirected Single-Source Shortest Paths with Positive Integer Weights in Linear Time}},
+ author={Thorup, Mikkel},
+ journal={Journal of the ACM},
+ volume={46},
+ number={3},
+ pages={362--394},
+ year={1999}
+}
+
+@article{ thorup:sssp,
+ author = {Mikkel Thorup},
+ title = {Integer priority queues with decrease key in constant time and the single source shortest paths problem},
+ journal = {Journal of Computer and System Sciences},
+ volume = {69},
+ number = {3},
+ year = {2004},
+ issn = {0022-0000},
+ pages = {330--353},
+ doi = {http://dx.doi.org/10.1016/j.jcss.2004.04.003},
+}
+
+@inproceedings{ hagerup:sssp,
+ author = {Torben Hagerup},
+ title = {{Improved Shortest Paths on the Word RAM}},
+ booktitle = {ICALP 2000: Proceedings of the 27th International Colloquium on Automata, Languages and Programming},
+ year = {2000},
+ isbn = {3-540-67715-1},
+ pages = {61--72},
+}
+
+@techreport { hakmem,
+ author = "Beeler, Michael and Gosper, R. William and Schroeppel, Rich",
+ title = "{HAKMEM}",
+ institution = "Massachusetts Institute of Technology",
+ year = "1972",
+ number = "239",
+ type = "Memo"
+}
+
+@book{ oxley:matroids,
+ title={{Matroid Theory}},
+ author={Oxley, J. G.},
+ year={1992},
+ publisher={Oxford University Press}
+}
+
+@article{ katoh:kmin,
+ author = {N. Katoh and T. Ibaraki and H. Mine},
+ title = {An Algorithm for Finding $K$ Minimum Spanning Trees},
+ year = {1981},
+ journal = {SIAM Journal on Computing},
+ volume = {10},
+ number = {2},
+ pages = {247--255},
+}
+
+@article{ chong:parallel,
+ author = {Ka Wong Chong and Yijie Han and Tak Wah Lam},
+ title = {Concurrent threads and optimal parallel minimum spanning trees algorithm},
+ journal = {Journal of the ACM},
+ volume = {48},
+ number = {2},
+ year = {2001},
+ issn = {0004-5411},
+ pages = {297--323},
+ doi = {http://doi.acm.org/10.1145/375827.375847},
+}
+
+@article{ moret:expmst,
+ title={{An Empirical Assessment of Algorithms for Constructing a Minimum Spanning Tree}},
+ author={Moret, B. M. E. and Shapiro, H. D.},
+ journal={Computational Support for Discrete Mathematics: DIMACS Workshop, March 12-14, 1992},
+ year={1994},
+ publisher={American Mathematical Society}
+}
+
+@article{ fredman:pairingheap,
+ title={{The pairing heap: A new form of self-adjusting heap}},
+ author={Fredman, M. L. and Sedgewick, R. and Sleator, D. D. and Tarjan, R. E.},
+ journal={Algorithmica},
+ volume={1},
+ number={1},
+ pages={111--129},
+ year={1986},
+}
+
+@inproceedings{ pettie:pairing,
+ author = {Seth Pettie},
+ title = {Towards a Final Analysis of Pairing Heaps},
+ booktitle = {FOCS 2005: Proceedings of the 46rd Annual IEEE Symposium on Foundations of Computer Science},
+ year = {2005},
+ pages = {174-183},
+}
+
+@book{ jaja:parallel,
+ title={{An introduction to parallel algorithms}},
+ author={J{\'a}J{\'a}, J.},
+ year={1992},
+ publisher={Addison Wesley Longman Publishing Co., Inc.}
+}
+
+@techreport { mm:ga,
+ author = "Martin Mare\v{s}",
+ title = "{Krajinou grafov\'ych algoritm\accent23u (Through the Landscape of Graph Algorithms)}",
+ institution = "Institut Teoretick\'e Informatiky",
+ address = "Praha, Czech Republic",
+ year = "2007",
+ number = "2007--330",
+ type = "ITI series",
+ note = {In Czech},
+}
+
+@book { horak:mofivefour,
+ author = {Hor\'ak, Karel and Mare\v{s}, Martin and Novotn\'y, Peter and \v{S}im\v{s}a, Jarom\'\i{}r and \v{S}vr\v{c}ek, Jaroslav and T\"opfer, Pavel and Zhouf, Jaroslav},
+ title = {54.~ro\v{c}n\'\i{}k matematick\'e olympi\'ady na st\v{r}edn\'\i{}ch \v{s}kol\'ach (The 54th Year of the Math Olympiad at High Schools)},
+ publisher = {Jednota \v{c}esk\'ych matematik\accent23u a fyzik\accent23u},
+ address = {Praha},
+ year = {2007},
+ note = {In Czech},
+ isbn = {80-7015-109-9},
+}
+
+@article{ tarjan:applpc,
+ author = {Robert Endre Tarjan},
+ title = {Applications of Path Compression on Balanced Trees},
+ journal = {Journal of the ACM},
+ volume = {26},
+ number = {4},
+ year = {1979},
+ issn = {0004-5411},
+ pages = {690--715},
+ doi = {http://doi.acm.org/10.1145/322154.322161},
+}
+
+@article{ kostochka:lbh,
+ title={{Lower bound of the Hadwiger number of graphs by their average degree}},
+ author={Kostochka, A. V.},
+ journal={Combinatorica},
+ volume={4},
+ number={4},
+ pages={307--316},
+ year={1984},
+}
+
+@article{ thomason:efc,
+ title={{An extremal function for contractions of graphs}},
+ author={Thomason, A.},
+ journal={Mathematical proceedings of the Cambridge Philosophical Society},
+ volume={95},
+ number={2},
+ pages={261--265},
+ year={1984},
+ publisher={Cambridge University Press}
}