两个二部Ramsey数的上界

Upper Bounds for Two Bipartite Ramsey Numbers

摘要:

给出对所有的整数n≥s≥3045,br(Ts,Kn,n)≤sn成立；以及对固定的整数t≥2,m≥1,br(Kt,t,Km,n)≤n+cn1-1/t成立,其中c>0是常数.另外,本文得到对正整数,br(Kt,t,Km,n-m),在这种情形下改进了下界r(Kt,t,Km,n-m)/2.

Abstract:

It is shown that br(Ts,Kn,n)≤sn for all integers n≥s≥3045, and br(Kt,t,Km,n)≤n+cn1-1/t for fixed integers t≥2,m≥1,where c>0 is a constant.Moreover,br(Kt,t,Km,n-m) for positive integers is obtained,which improves the lower bound r(Kt,t,Km,n-m)/2.