Asymptotic Upper Bounds for Ramsey Functions

被引：0

作者：

Yusheng Li

Cecil C. Rousseau

Wenan Zang

机构：

[1] Department of Mathematics and Physics,

[2] Hehai University,undefined

[3] Nanjing,undefined

[4] Jiangsu 210098,undefined

[5] P. R. China,undefined

[6] Department of Mathematical Sciences,undefined

[7] The University of Memphis,undefined

[8] Memphis,undefined

[9] TN 38152,undefined

[10] USA,undefined

[11] Department of Mathematics,undefined

[12] The University of Hong Kong,undefined

[13] Hong Kong,undefined

[14] P. R. China e-mail: wzang@maths.hku.hk,undefined

来源：

Graphs and Combinatorics | 2001年 / 17卷

关键词：

Key words. Ramsey number; Independence number; Average degree; Convex function;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We show that for any graph G with N vertices and average degree d, if the average degree of any neighborhood induced subgraph is at most a, then the independence number of G is at least Nfa+1(d), where fa+1(d)=∫01(((1−t)1/(a+1))/(a+1+(d−a−1)t))dt. Based on this result, we prove that for any fixed k and l, there holds r(Kk+l,Kn)≤ (l+o(1))nk/(logn)k−1. In particular, r(Kk, Kn)≤(1+o(1))nk−1/(log n)k−2.

引用

页码：123 / 128

页数：5

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