Highly Connected Subgraphs with Large Chromatic Number

IF 0.9 3区数学 Q2 MATHEMATICS SIAM Journal on Discrete Mathematics Pub Date : 2024-01-09 DOI:10.1137/22m150040x

Tung H. Nguyen

引用次数: 0

Abstract

SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 243-260, March 2024.
Abstract. For integers [math] and [math], let [math] be the least integer [math] such that every graph with chromatic number at least [math] contains a [math]-connected subgraph with chromatic number at least [math]. Refining the recent result of Girão and Narayanan [Bull. Lond. Math. Soc., 54 (2022), pp. 868–875] that [math] for all [math], we prove that [math] for all [math] and [math]. This sharpens earlier results of Alon et al. [J. Graph Theory, 11 (1987), pp. 367–371], of Chudnovsky [J. Combin. Theory Ser. B, 103 (2013), pp. 567–586], and of Penev, Thomassé, and Trotignon [SIAM J. Discrete Math., 30 (2016), pp. 592–619]. Our result implies that [math] for all [math], making a step closer towards a conjecture of Thomassen [J. Graph Theory, 7 (1983), pp. 261–271] that [math], which was originally a result with a false proof and was the starting point of this research area.

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色度数大的高连接子图

SIAM 离散数学杂志》第 38 卷第 1 期第 243-260 页，2024 年 3 月。摘要。对于整数[math]和[math]，设[math]是最小整数[math]，使得每个色度数至少为[math]的图都包含一个色度数至少为[math]的[math]连接子图。在完善吉朗和纳拉亚南[Bull. Lond. Math. Soc., 54 (2022), pp. 868-875]关于[math]为所有[math]的最新结果的基础上，我们证明[math]为所有[math]和[math]。这使 Alon 等人 [J. Graph Theory, 11 (1987), pp. 367-371]、Chudnovsky [J. Combin. Theory Ser. B, 103 (2013), pp.我们的结果意味着[math]适用于所有[math]，从而向托马森[J. Graph Theory, 7 (1983), pp. 261-271]的猜想[math]又迈近了一步，这个猜想原本是一个假证明的结果，是这一研究领域的起点。

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来源期刊

SIAM Journal on Discrete Mathematics 数学-应用数学

CiteScore

1.90

自引率

0.00%

发文量

124

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Discrete Mathematics (SIDMA) publishes research papers of exceptional quality in pure and applied discrete mathematics, broadly interpreted. The journal''s focus is primarily theoretical rather than empirical, but the editors welcome papers that evolve from or have potential application to real-world problems. Submissions must be clearly written and make a significant contribution. Topics include but are not limited to: properties of and extremal problems for discrete structures combinatorial optimization, including approximation algorithms algebraic and enumerative combinatorics coding and information theory additive, analytic combinatorics and number theory combinatorial matrix theory and spectral graph theory design and analysis of algorithms for discrete structures discrete problems in computational complexity discrete and computational geometry discrete methods in computational biology, and bioinformatics probabilistic methods and randomized algorithms.

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