On the Ramsey numbers for the tree graphs versus certain generalised wheel graphs

被引:1
|
作者
Chng, Zhi Yee [1 ]
Tan, Ta Sheng [2 ]
Wong, Kok Bin [2 ]
机构
[1] UNSW Sydney, Sch Math & Stat, Sydney, NSW 2052, Australia
[2] Univ Malaya, Inst Math Sci, Kuala Lumpur 50603, Malaysia
关键词
Ramsey number; Tree; Generalised wheel graphs; STARS; PATHS; ORDER;
D O I
10.1016/j.disc.2021.112440
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Given two simple graphs G and H, the Ramsey number R(G, H) is the smallest integer n such that for any graph of order n, either it contains G or its complement contains H. Let T-n be a tree graph of order n and W-s,W-m be the generalised wheel graph K-s + C-m. In this paper, we show that for n >= 5, s >= 2, R(T-n, W-s,W- 6) = (s + 1)(n - 1) + 1 and for n >= 5, s >= 1, R(T-n, W-s,W-7) = (s + 2)(n - 1) + 1. We also determine the exact value of R(T-n, W-s,W-m) for large nand s. (C) 2021 Elsevier B.V. All rights reserved.
引用
收藏
页数:12
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