Improved bounds on the Ramsey number of fans

被引：4

作者：

Chen, Guantao ^{[1
]}

Yu, Xiaowei ^{[2
]}

Zhao, Yi ^{[1
]}

机构：

[1] Georgia State Univ, Dept Math & Stat, Atlanta, GA 30303 USA

[2] Jiangsu Normal Univ, Dept Math & Stat, Xuzhou 221116, Peoples R China

来源：

EUROPEAN JOURNAL OF COMBINATORICS | 2021年 / 96卷

基金：

中国国家自然科学基金; 美国国家科学基金会;

关键词：

D O I：

10.1016/j.ejc.2021.103347

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a given graph H, the Ramsey number r(H) is the minimum N such that any 2-edge-coloring of the complete graph K-N yields a monochromatic copy of H. Given a positive integer n, a fanF(n) is a graph formed by n triangles that share one common vertex. We show that 9n/2-5 <= r(F-n) < 11n/2+6 for any n. This improves previous best bounds r(F-n) <= 6n of Lin and Li and r(F-n) >= 4n+2 of Zhang, Broersma and Chen. (C) 2021 Elsevier Ltd. All rights reserved.

引用

页数：7