The Ramsey numbers for disjoint unions of trees
The Ramsey numbers for disjoint unions of trees
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树不相交并集的拉姆齐数
DOI：
10.1016/j.disc.2006.06.011
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发表时间：
2006
期刊：
影响因子：
--
通讯作者：
H. Assiyatun
中科院分区：
文献类型：
--
作者：
E. Baskoro;Hasmawati;H. Assiyatun
对于给定的图G和H，Ramsey数R（G，H）是最小的自然数n，使得对任意n阶图F：F包含G或F的补图包含H.本文研究了Ramsey数R（G，H），其中G是树，H是轮，W或完全图Km.本文证明了当n ≥ 3时，当k ≥ 2，n为偶数时，R（kSn，W 4）=（k+1）n;当k ≥ 1，n为奇数时，R（kSn，W 4）=（k+1）n-1.我们还证明了[公式：见正文]。
For given graphs G and H, the Ramsey numberR(G,H) is the smallest natural number n such that for every graph F of order n: either F contains G or the complement of F contains H. In this paper, we investigate the Ramsey number R(∪G,H), where G is a tree and H is a wheel Wmor a complete graph Km. We show that if n⩾3, then R(kSn,W4)=(k+1)n for k⩾2, even n and R(kSn,W4)=(k+1)n-1 for k⩾1 and odd n. We also show that [Formula: see text] .