On the size-Ramsey number of grids

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

Combinatorics, Probability & Computing Pub Date : 2023-06-26 DOI:10.1017/s0963548323000147

David Conlon, Rajko Nenadov, Miloš Trujić

引用次数: 6

Abstract

Abstract We show that the size-Ramsey number of the $\sqrt{n} \times \sqrt{n}$ grid graph is $O(n^{5/4})$ , improving a previous bound of $n^{3/2 + o(1)}$ by Clemens, Miralaei, Reding, Schacht, and Taraz.

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关于网格的大小拉姆齐数

摘要我们证明了$\sqrt{n} \乘以\sqrt{n}$网格图的size-Ramsey数为$O(n^{5/4})$，改进了Clemens, Miralaei, Reding, Schacht和Taraz先前的$n^{3/2 + O(1)}$的边界。

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.