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
收藏
页数：7
相关论文
共 50 条
  • [11] Improved upper and lower bounds on a geometric Ramsey problem
    Lavrov, Mikhail
    Lee, Mitchell
    Mackey, John
    EUROPEAN JOURNAL OF COMBINATORICS, 2014, 42 : 135 - 144
  • [12] BOUNDS FOR THE RAMSEY NUMBER OF A DISCONNECTED GRAPH VERSUS ANY GRAPH
    GOULD, RJ
    JACOBSON, MS
    JOURNAL OF GRAPH THEORY, 1982, 6 (04) : 413 - 417
  • [13] New lower bounds on the size-Ramsey number of a path
    Bal, Deepak
    DeBiasio, Louis
    ELECTRONIC JOURNAL OF COMBINATORICS, 2022, 29 (01):
  • [14] Improved bounds on the multicolor Ramsey numbers of paths and even cycles
    Knierim, Charlotte
    Su, Pascal
    ELECTRONIC JOURNAL OF COMBINATORICS, 2019, 26 (01):
  • [15] A NOTE ON RAMSEY NUMBERS FOR FANS
    Zhang, Yanbo
    Broersma, Hajo
    Chen, Yaojun
    BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2015, 92 (01) : 19 - 23
  • [16] Luus-Jaakola Optimization Procedure for Ramsey Number Lower Bounds
    Mange, Jeremy
    Dunn, Andrew
    INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE, 2015, 10 (01): : 57 - 68
  • [17] Improved bounds on the domination number of a tree
    Desormeaux, Wyatt J.
    Haynes, Teresa W.
    Henning, Michael A.
    DISCRETE APPLIED MATHEMATICS, 2014, 177 : 88 - 94
  • [18] Improved bounds for the chromatic number of a graph
    Hakimi, SL
    Schmeichel, E
    JOURNAL OF GRAPH THEORY, 2004, 47 (03) : 217 - 225
  • [19] Improved bounds for the extremal number of subdivisions
    Janzer, Oliver
    ELECTRONIC JOURNAL OF COMBINATORICS, 2019, 26 (03):
  • [20] Improved Upper Bounds on the Crossing Number
    Dujmovic, Vida
    Kawarabayashi, Ken-ichi
    Mohar, Bojan
    Wood, David R.
    PROCEEDINGS OF THE TWENTY-FOURTH ANNUAL SYMPOSIUM ON COMPUTATIONAL GEOMETRY (SGG'08), 2008, : 375 - 384
12345