Upper Bounds on the Multicolor Ramsey Numbers rk(C4)

被引：0

作者：

Li, Tian-yu ^{[1
]}

Lin, Qi-zhong ^{[1
]}

机构：

[1] Fuzhou Univ, Ctr Discrete Math, Fuzhou 350108, Peoples R China

来源：

ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES | 2025年 / 41卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Multicolor Ramsey number; Tur & aacute; n number; 4-cycle; GRAPHS;

D O I：

10.1007/s10255-023-1074-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The multicolor Ramsey number rk(C4) is the smallest integer N such that any k-edge coloring of KN contains a monochromatic C4. The current best upper bound of rk(C4) was obtained by Chung (1974) and independently by Irving (1974), i.e., rk(C4) <= k2 + k + 1 for all k >= 2. There is no progress on the upper bound since then. In this paper, we improve the upper bound of rk(C4) by showing that rk(C4) <= k2 + k - 1 for even k >= 6. The improvement is based on the upper bound of the Tur & aacute;n number ex(n, C4), in which we mainly use the double counting method and many novel ideas from Firke, Kosek, Nash, and Williford [J. Combin. Theory, Ser. B 103 (2013), 327-336].

引用

页码：286 / 294

页数：9