More fixes to bugs reported by Patrice.

diff --git a/TODO b/TODO
index cb7c13b7f172055a661928174edd615dd36ed1f8..b3291cadf83b681e48ec48c01b46193e3aea333c 100644 (file)
--- a/TODO
+++ b/TODO
@@ -25,11 +25,6 @@ Diaz:
 Patrice:
 
 > Remark on 2.5.1: polynomial time could be replaced by sub-exponential time.
-- For 1.5.6, you should probably quote D. Cheriton and R.E. Tarjan.
-  Finding Minimum Spanning Trees. SIAM J. on Comp. 5(4) (1976) pp.
-  724-742. who gave a linear time algorithm for planar graphs, extended by
-  Tarjan in 1983 to proper minor closed classes (both quoted by Gustedt).
-  [XXX: The paper should be in the library at MS.]
 > In 3.1.12 and 3.1.16, you should make explicit the dependence of the
   running time  with respect, for instance, to the Hadwiger number of the
   graph or to the maximal density nabla(G) of a minor of the graph, as

diff --git a/adv.tex b/adv.tex
index 35d5d9b685a558f1bd8d9c627ccdff3c88d7981f..2a81be339ee37a25dc2d122741ec139154d641b4 100644 (file)
--- a/adv.tex
+++ b/adv.tex
@@ -125,7 +125,7 @@ $G$~would contain a~subdivision of~$K_x$ and hence $K_x$ as a~minor.
 
 Let us return to the analysis of our algorithm.
 
-\thmn{MST on minor-closed classes, Mare\v{s} \cite{mm:mst}}\id{mstmcc}%
+\thmn{MST on minor-closed classes, Tarjan \cite{tarjan:dsna}}\id{mstmcc}%
 For any fixed non-trivial minor-closed class~$\cal C$ of graphs, the Contractive Bor\o{u}vka's
 algorithm (\ref{contbor}) finds the MST of any graph of this class in time
 $\O(n)$. (The constant hidden in the~$\O$ depends on the class.)
@@ -256,8 +256,8 @@ has degree~9.
 \figure{hexangle.eps}{\epsfxsize}{The construction from Remark~\ref{hexa}}
 
 \rem
-The observation in~Theorem~\ref{mstmcc} was also independently made by Gustedt \cite{gustedt:parallel},
-who studied a~parallel version of the Contractive Bor\o{u}vka's algorithm applied
+The observation in~Theorem~\ref{mstmcc} was also used by Gustedt \cite{gustedt:parallel},
+to construct parallel version of the Contractive Bor\o{u}vka's algorithm applied
 to minor-closed classes.
 
 \rem

diff --git a/biblio.bib b/biblio.bib
index ad43a453bfcdbade05cd86e3950d330032cb0bd3..a21c1c0380de3434b15c4a5cc8e4ad7762a6ff7f 100644 (file)
--- a/biblio.bib
+++ b/biblio.bib
@@ -1588,3 +1588,13 @@
   volume={1675},
   series={{Lecture Notes in Math}},
 }
+
+@article{ cheriton:mst,
+  title={{Finding Minimum Spanning Trees}},
+  author={Cheriton, D. and Tarjan, R.E.},
+  journal={SIAM Journal on Computing},
+  volume={5},
+  number={4},
+  pages={724--742},
+  year={1976},
+}

diff --git a/mst.tex b/mst.tex
index 8a6a12a278b66ac23924bcbcf551e06a618ee5fb..d4bf95284cb8546ded9c9ba0eda197f475c1cdc5 100644 (file)
--- a/mst.tex
+++ b/mst.tex
@@ -654,7 +654,7 @@ in all iterations is $\O(\sum_i n_i^2) = \O(\sum_i n^2/4^i) = \O(n^2)$.
 
 On planar graphs, the algorithm runs much faster:
 
-\thmn{Contractive Bor\o{u}vka on planar graphs}\id{planarbor}%
+\thmn{Contractive Bor\o{u}vka's algorithm on planar graphs, Cheriton and Tarjan \cite{cheriton:mst}}\id{planarbor}%
 When the input graph is planar, the Contractive Bor\o{u}vka's algorithm runs in
 time $\O(n)$.
 

diff --git a/pref.tex b/pref.tex
index cdff6b455e030e26f8a6853493ae42544b60e60d..c06716c95f9f2ff61e1c76c02c85fa70791dda5b 100644 (file)
--- a/pref.tex
+++ b/pref.tex
@@ -37,7 +37,7 @@ included in the textbook \cite{mm:ga} which I have written for this course.
 \itemize\ibull
 \:The lower bound in Section \ref{contalg}. Not published yet.
 \:The tree isomorphism algorithm in Section \ref{bucketsort}. Not published yet.
-\:Both algorithms for minor-closed graph classes in Section \ref{minorclosed}. Published in \cite{mm:mst}.
+\:One of the algorithms for minor-closed graph classes in Section \ref{minorclosed}. Published in \cite{mm:mst}.
 \:The linear-time verification algorithm in Section \ref{verifysect} is a~simplification
   of the algorithm of King \cite{king:verifytwo} and it corrects many omissions
   in the original paper. Not published yet.