含双参数的Ramsey数新上、下界公式

摘要

本文得到了含双参数x,y的Ramsey数的新上、下界公式,且初步研究了它的应用,证明了R(K6-e,K6)≤116和R(K6-e,K7)≤202.%The Ramsey number R(G1, G2) is the smallest integer p such that for any graph G on p vertices either G contains G1 or -G contains G2, where -G denotes the complement of G.In this paper, some new bounds with two parameters for the Ramsey number R(G1,G2),under some assumptions, are obtained. Especially, we prove that R(K6 - e, K6) ≤ 116and R(K6 - e, K7) ≤ 202, these improve the two upper bounds for the classical Ramsey number in [5].