Ramsey Numbers for Complete Graphs Versus Generalized Fans

被引:1
作者
Wang, Maoqun [1 ]
Qian, Jianguo [1 ]
机构
[1] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China
基金
中国国家自然科学基金;
关键词
Ramsey number; Star-critical Ramsey number; Complete graph; Generalized fan;
D O I
10.1007/s00373-022-02590-z
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
For two graphs G and H, let r(G, H) and r(*)(G, H) denote the Ramsey number and star-critical Ramsey number of G versus H, respectively. In 1996, Li and Rousseau proved that r(K-m, F-t,F-n) = tn(m - 1) + 1 for m >= 3 and sufficiently large n, where F-t,F-n = K-1 + nK(t). Recently, Hao and Lin proved that r(K-3, F-3,F-n) = 6n + 1 for n >= 3 and r(*)(K-3, F-3,F-n) = 3n + 3 for n >= 4. In this paper, we show that r(K-m, sF(t,n)) = tn(m + s - 2) + s for sufficiently large n and, in particular, r(K-3, sF(t,n)) = tn(s + 1) + s for t is an element of {3, 4}, n >= t and s >= 1. We also show that r*(K-3, F-4,F-n) = 4n + 4 for n >= 4 and establish an upper bound for r(F-2,F-m, F-t,F-n).
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页数:8
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