On Ramsey Numbers for Trees Versus Wheels of Five or Six Vertices

被引：0

作者：

E.T. Baskoro

S.M. Surahmat

M. Nababan

机构：

[1] Department of Mathematics,

[2] Institut Teknologi Bandung,undefined

[3] Jalan Ganesa 10 Bandung,undefined

[4] Indonesia. e-mails: {ebaskoro,undefined

[5] kana_s,undefined

[6] nababan}@dns.math.itb.ac.id,undefined

[7] Department of Computer Science and Software Engineering,undefined

[8] The University of Newcastle,undefined

[9] Callaghan,undefined

[10] NSW 2308,undefined

[11] Australia. e-mail: mirka@cs.newcastle.edu.au,undefined

来源：

Graphs and Combinatorics | 2002年 / 18卷

关键词：

Positive Integer; Open Problem; Tree Versus; Small Positive Integer; Ramsey Number;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

For given two graphs G dan H, the Ramsey numberR(G,H) is the smallest positive integer n such that every graph F of order n must contain G or the complement of F must contain H. In [12], the Ramsey numbers for the combination between a star Sn and a wheel Wm for m=4,5 were shown, namely, R(Sn,W4)=2n−1 for odd n and n≥3, otherwise R(Sn,W4)=2n+1, and R(Sn,W5)=3n−2 for n≥3. In this paper, we shall study the Ramsey number R(G,Wm) for G any tree Tn. We show that if Tn is not a star then the Ramsey number R(Tn,W4)=2n−1 for n≥4 and R(Tn,W5)=3n−2 for n≥3. We also list some open problems.

引用

页码：717 / 721

页数：4