More fixes after JN's feedback.

diff --git a/adv.tex b/adv.tex
index eca96fdd55ad425b02579bb984e8cf4af76aad01..2138d7fdbae551cefb4138815bb5f3993743047c 100644 (file)
--- a/adv.tex
+++ b/adv.tex
@@ -258,11 +258,6 @@ has degree~9.
 
 \figure{hexangle.eps}{\epsfxsize}{The construction from Remark~\ref{hexa}}
 
-\rem
-Minor-closed classes share many other interesting properties, for example bounded chromatic
-numbers of various kinds, as shown by Theorem 6.1 of \cite{nesetril:minors}. We can expect
-that many algorithmic problems will turn out to be easy for them.
-
 %--------------------------------------------------------------------------------
 
 \section{Iterated algorithms}\id{iteralg}%

diff --git a/appl.tex b/appl.tex
index 0b1b302ec84cefa0148ac3686881321f0cfab8c9..4f7c04bc31a75d99686390fe8b7c445943241d04 100644 (file)
--- a/appl.tex
+++ b/appl.tex
@@ -113,7 +113,9 @@ each other only in the given points looks artificial and it is indeed uncommon i
 practical applications (including the problem of designing electrical transmission
 lines originally studied by Bor\o{u}vka). If we lift this restriction, we get
 the problem known by the name Steiner tree.\foot{It is named after the Swiss mathematician
-Jacob Steiner who studied a~special case of this problem in the 19th century.}
+Jacob Steiner who studied a~special case of this problem in the 19th century.
+The complete problem can be traced to Jarn\'\i{}k and K\"ossler \cite{jarnik:steiner}
+and even to K.~F.~Gauss. See \cite{korte:jarnik} for its history.}
 We can also define it in terms of graphs:
 
 \defn A~\df{Steiner tree} of a~weighted graph~$(G,w)$ with a~set~$M\subseteq V$

diff --git a/biblio.bib b/biblio.bib
index 5b86570a51e4cd691506b8d8b6df76514ff27ccd..7633a8d2c4f05d5f3ef4473eef72cb6dd8a3adfe 100644 (file)
--- a/biblio.bib
+++ b/biblio.bib
@@ -106,7 +106,7 @@
 @article{ nesetril:history,
     author = "Jaroslav Ne{\v{s}}et{\v{r}}il",
     title = "{Some remarks on the history of MST-problem}",
-    journal = "Archivum Mathematicum",
+    journal = "Archivum Mathematicum (Brno)",
     publisher = "Masaryk University",
     address = "Brno, Czech Republic",
     volume = "33",
@@ -246,7 +246,7 @@
 @article { mm:mst,
    author = "Martin Mare\v{s}",
    title = "{Two linear time algorithms for MST on minor closed graph classes}",
-   journal = "{Archivum Mathematicum}",
+   journal = "{Archivum Mathematicum (Brno)}",
    publisher = "Masaryk University",
    address = "Brno, Czech Republic",
    volume = "40",
@@ -1583,8 +1583,7 @@
   title={{Probability Theory of Classical Euclidean Optimization Problems}},
   author={Yukich, J.E.},
   year={1998},
-  publisher={Springer},
-  publisher = {Springer Verlag},
+  publisher={Springer Verlag},
   volume={1675},
   series={{Lecture Notes in Math}},
 }
@@ -1605,3 +1604,22 @@
   school={{Charles University in Prague, Faculty of Math and Physics}},
   year={2008},
 }
+
+@article{ jarnik:steiner,
+  author={Jarn\'\i{}k, V. and K\"ossler, M.},
+  title={O minim\' aln\'{\i}ch grafech obsahuj\'{\i}c\'{\i}ch danou mno\v zinu bod\accent23 u},
+  journal={\v Casopis pro p\v estov\'an\'\i{} matematiky},
+  volume={63},
+  year={1964},
+  pages={223--225},
+  note="In Czech"
+}
+
+@article{ korte:jarnik,
+  author={Korte, B. and Ne\v{s}et\v{r}il, J.},
+  title={{Vojt\v{e}ch Jarn\'\i{}k's work in combinatorial optimization}},
+  journal={Discrete Mathematics},
+  volume={235},
+  pages={1--17},
+  year={2001},
+}

diff --git a/mst.tex b/mst.tex
index 6d97dc101126384f1043fc035e092968ec5f1b9b..0805475abc9d80ecdfbc5737bb79cd4c0a32bf55 100644 (file)
--- a/mst.tex
+++ b/mst.tex
@@ -57,8 +57,10 @@ mosaic.
 When compared with the earlier surveys on the minimum spanning trees, most
 notably Graham and Hell \cite{graham:msthistory} and Eisner \cite{eisner:tutorial},
 this work adds many of the recent advances, the dynamic algorithms and
-also the relationship with computational models. It is based on the author's
-PhD thesis \cite{mm:thesis}.
+also the relationship with computational models. We tried to be self-contained
+and to include proofs of the main results, including the low-level details
+where they are important. This paper is based on a~part of the author's PhD thesis
+\cite{mm:thesis}.
 
 \nota
 We have tried to stick to the usual notation except where it was too inconvenient.