The size-Ramsey number of trees

被引:14
|
作者
Dellamonica, Domingos, Jr. [1 ]
机构
[1] Emory Univ, Dept Math, Atlanta, GA 30322 USA
关键词
size-Ramsey number; trees; expander graphs; BOUNDED DEGREE; GRAPHS;
D O I
10.1002/rsa.20363
中图分类号
TP31 [计算机软件];
学科分类号
081202 ; 0835 ;
摘要
Given a graph G, the size-Ramsey number (r) over cap (G) is the minimum number m for which there exists a graph F on m edges such that any two-coloring of the edges of F admits a monochromatic copy of G. In 1983, J. Beck introduced an invariant beta(.) for trees and showed that (r) over cap (T) = Omega(beta(T)). Moreover he conjectured that (r) over cap (T) = Theta(beta(T)). We settle this conjecture by providing a family of graphs and an embedding scheme for trees. (C) 2011 Wiley Periodicals, Inc. Random Struct. Alg., 40, 49-73, 2012
引用
收藏
页码:49 / 73
页数:25
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