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.
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页数：7
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