On Ramsey Numbers for Trees Versus Wheels of Five or Six Vertices
On Ramsey Numbers for Trees Versus Wheels of Five or Six Vertices
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DOI：
10.1007/s003730200056
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发表时间：
2002-12
影响因子：
0.7
通讯作者：
E. Baskoro;Surahmat;S. M. Nababan;Mirka Miller
中科院分区：
文献类型：
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作者：
E. Baskoro;Surahmat;S. M. Nababan;Mirka Miller
对于给定的两个图sgdanh，拉姆齐数r （G，H）是最小的正整数，使得每一个有序的图f都必须包含G或补数off必须包含H。在[12]中，群星与车轮wmform =4,5的组合的Ramsey数，即当奇数≥3时R(Sn,W4)=2n−1，当奇数≥3时R(Sn,W4)=2n+1，当奇数≥3时R(Sn,W5)=3n−2。本文研究任意树的拉姆齐数r （G,Wm）。我们证明了如果tni不是恒星，那么Ramsey数r (Tn,W4)=2n−1 form≥4,r (Tn,W5)=3n−2 form≥3。我们还列出了一些尚未解决的问题。
For given two graphsGdanH, theRamsey numberR(G,H) is the smallest positive integernsuch that every graphFof ordernmust containGor the complement ofFmust containH. In [12], the Ramsey numbers for the combination between a starSnand a wheelWmform=4,5 were shown, namely,R(Sn,W4)=2n−1 for oddnandn≥3, otherwiseR(Sn,W4)=2n+1, andR(Sn,W5)=3n−2 forn≥3. In this paper, we shall study the Ramsey numberR(G,Wm) forGany treeTn. We show that ifTnis not a star then the Ramsey numberR(Tn,W4)=2n−1 forn≥4 andR(Tn,W5)=3n−2 forn≥3. We also list some open problems.