The Ramsey numbers of wheels versus odd cycles
The Ramsey numbers of wheels versus odd cycles
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DOI：
10.1016/j.disc.2014.01.017
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发表时间：
2014-05
期刊：
影响因子：
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通讯作者：
Yanbo Zhang;Yunqing Zhang;Yaojun Chen
中科院分区：
文献类型：
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作者：
Yanbo Zhang;Yunqing Zhang;Yaojun Chen
给定两个图G1和G2，Ramsey数R(G1，G2)是最小整数N，使得对任一N阶图G，G包含G1或其补图包含G2.设Cm表示m阶圈，Wn是n+1阶轮.本文证明了：对m阶圈，n≥3(m−1)/2和(m，n)≠(3，3)，(3，4)，R(Wn，对于m，n奇数和m<，Cm)=3m−2；N≤3(m−1)/2。
Given two graphs G 1 and G 2, the Ramsey number R (G 1, G 2) is the smallest integer N such that for any graph G of order N, either G contains G 1 or its complement contains G 2. Let C m denote a cycle of order m and W n a wheel of order n+ 1. In this paper, it is shown that R (W n, C m)= 2 n+ 1 for m odd, n≥ 3 (m− 1)/2 and (m, n)≠(3, 3),(3, 4), and R (W n, C m)= 3 m− 2 for m, n odd and m< n≤ 3 (m− 1)/2.