Branch-width and well-quasi-ordering in matroids and graphs

被引：64
|
作者：
Geelen, JF [1 ]
Gerards, AMH
Whittle, G
机构：
[1] Univ Waterloo, Dept Combinator & Optimizat, Waterloo, ON N2L 3G1, Canada
[2] CWI, NL-1090 GB Amsterdam, Netherlands
[3] Eindhoven Univ Technol, Dept Math & Comp Sci, NL-5600 MB Eindhoven, Netherlands
[4] Univ Victoria, Sch Math & Comp Sci, Wellington, New Zealand
来源：
JOURNAL OF COMBINATORIAL THEORY SERIES B | 2002年 / 84卷 / 02期
基金：
加拿大自然科学与工程研究理事会;
关键词：
matroids; graphs; minors; finite fields; connectivity; submodularity; branch-width; tree-width; well-quasi-ordering;
D O I：
10.1006/jctb.2001.2082
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove that a class of matroids representable over a fixed finite field and with bounded branch-width is well-quasi-ordered under taking minors. With some extra work. the result implies Robertson and Seymour's result that graphs with bounded tree-width (or equivalently, bounded branch-width) are well-quasi-ordered under taking minors. We will not only derive their result from our result on matroids, but we will also use the main tools for a direct proof that graphs with bounded branch-width are well-quasi-ordered under taking minors. This proof also provides a model for the proof of the result on matroids, with all specific matroid technicalities stripped off. (C) 2002 Elsevier Science (USA).
引用
收藏
页码：270 / 290
页数：21
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