On Ramsey minimal graphs

被引：12

作者：

Rodl, V. ^{[1
]}

Siggers, M. ^{[2
]}

机构：

[1] Emory Univ, Dept Math & Comp Sci, Atlanta, GA 30322 USA

[2] Simon Fraser Univ, Sch Comp Sci, Burnaby, BC V5A 1S6, Canada

来源：

SIAM JOURNAL ON DISCRETE MATHEMATICS | 2008年 / 22卷 / 02期

基金：

美国国家科学基金会;

关键词：

Ramsey-minimal; Ramsey infinite; sender;

D O I：

10.1137/050647116

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A graph G is r-Ramsey-minimal with respect to a graph H if every r-coloring of the edges of G yields a monochromatic copy of H, but the same is not true for any proper subgraph of G. In this paper we show that for any integer k >= 3 and r >= 2, there exists a constant c > 1 such that for large enough n, there exist at least c(n2) nonisomorphic graphs on at most n vertices, each of which is r-Ramsey-minimal with respect to the complete graph K(k). Furthermore, in the case r = 2, we give an asymmetric version of the above result.

引用

页码：467 / 488

页数：22

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