A Property on Monochromatic Copies of Graphs Containing a Triangle

IF 0.9 3区数学 Q2 MATHEMATICS

SIAM Journal on Discrete Mathematics Pub Date : 2024-01-12 DOI:10.1137/23m1564894

Hao Chen, Jie Ma

引用次数: 0

Abstract

SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 316-326, March 2024.
Abstract. A graph [math] is called common and, respectively, strongly common if the number of monochromatic copies of [math] in a 2-edge-coloring [math] of a large clique is asymptotically minimized by the random coloring with an equal proportion of each color and, respectively, by the random coloring with the same proportion of each color as in [math]. A well-known theorem of Jagger, Št’ovíček, and Thomason states that every graph containing a [math] is not common. Here we prove an analogous result that every graph containing a [math] and with at least four edges is not strongly common.

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包含三角形的图形单色副本的性质

SIAM 离散数学杂志》，第 38 卷第 1 期，第 316-326 页，2024 年 3 月。摘要。如果在一个大的簇的 2 边着色[math]中，[math]的单色副本数被每种颜色比例相等的随机着色和每种颜色比例与[math]相同的随机着色渐近地最小化，则图[math]分别称为普通图和强普通图。贾格尔、什特奥维切克和托马森的一个著名定理指出，每个包含一个[math]的图都是不常见的。在这里，我们证明了一个类似的结果，即每个包含一个[math]且至少有四条边的图都不是强公共图。

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.