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：
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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.
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页码：123 / 128
页数：5
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