The Excluded Tree Minor Theorem Revisited

IF 0.9 4区数学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Combinatorics, Probability & Computing Pub Date : 2023-09-27 DOI:10.1017/s0963548323000275

Vida Dujmović, Robert Hickingbotham, Gwenaël Joret, Piotr Micek, Pat Morin, David R. Wood

引用次数: 0

Abstract

Abstract We prove that for every tree $T$ of radius $h$ , there is an integer $c$ such that every $T$ -minor-free graph is contained in $H\boxtimes K_c$ for some graph $H$ with pathwidth at most $2h-1$ . This is a qualitative strengthening of the Excluded Tree Minor Theorem of Robertson and Seymour (GM I). We show that radius is the right parameter to consider in this setting, and $2h-1$ is the best possible bound.

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重新考察排除树小定理

摘要证明了对于每棵半径为$h$的树$T$，存在一个整数$c$，使得对于路径宽度不超过$2h-1$的图$h$，每一个$T$无次图$都包含在$h \box * K_c$中。这是对Robertson和Seymour的排除树小定理(GM I)的定性强化。我们证明了半径是在这种情况下考虑的正确参数，并且$2h-1$是最好的可能界。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Combinatorics, Probability & Computing 数学-计算机：理论方法

CiteScore

2.40

自引率

11.10%

发文量

审稿时长

6-12 weeks

期刊介绍： Published bimonthly, Combinatorics, Probability & Computing is devoted to the three areas of combinatorics, probability theory and theoretical computer science. Topics covered include classical and algebraic graph theory, extremal set theory, matroid theory, probabilistic methods and random combinatorial structures; combinatorial probability and limit theorems for random combinatorial structures; the theory of algorithms (including complexity theory), randomised algorithms, probabilistic analysis of algorithms, computational learning theory and optimisation.