两个二部Ramsey数的上界

Upper Bounds for Two Bipartite Ramsey Numbers

给出对所有的整数n≥s≥3 0 4 5,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.

It is shown that br（Ts,Kn,n）≤sn for all integers n≥ s≥3045, and br（Kt,t, Km,n ） ≤ n ＋ cn^1-1/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 （K t,t, K,m,n-m ）/2.