On Ramsey Size-Linear Graphs and Related Questions

IF 0.9 3区数学 Q2 MATHEMATICS

SIAM Journal on Discrete Mathematics Pub Date : 2024-01-09 DOI:10.1137/22m1481713

Domagoj Bradač, Lior Gishboliner, Benny Sudakov

引用次数: 0

Abstract

SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 225-242, March 2024.
Abstract. In this paper we prove several results on Ramsey numbers [math] for a fixed graph [math] and a large graph [math], in particular for [math]. These results extend earlier work of Erdős, Faudree, Rousseau, and Schelp and of Balister, Schelp, and Simonovits on so-called Ramsey size-linear graphs. Among other results, we show that if [math] is a subdivision of [math] with at least six vertices, then [math] for every graph [math]. We also conjecture that if [math] is a connected graph with [math], then [math]. The case [math] was proved by Erdős, Faudree, Rousseau, and Schelp. We prove the case [math].

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论拉姆齐大小线性图及相关问题

SIAM 离散数学杂志》，第 38 卷，第 1 期，第 225-242 页，2024 年 3 月。摘要在本文中，我们证明了关于固定图[math]和大图[math]的拉姆齐数[math]，特别是[math]的拉姆齐数[math]的几个结果。这些结果扩展了 Erdős、Faudree、Rousseau 和 Schelp 以及 Balister、Schelp 和 Simonovits 早期关于所谓拉姆齐大小线性图的工作。在其他结果中，我们证明了如果 [math] 是至少有六个顶点的 [math] 的细分图，那么 [math] 对于每个图 [math]。我们还猜想，如果[math]是[math]的连通图，那么[math]。Erdős, Faudree, Rousseau 和 Schelp 证明了 [math] 的情况。我们证明了 [math] 的情况。

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

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.