关于完全三部图的Ramsey数

Complete Three-partite-graph Ramsey Number

该文对完全三部图的Ramsey数r(kt,m,n,kn)的上界进行了研究。将自然数集划分为2类集合{n′}和{n″},用高斯超几何函数表示独立数的下界。证明了r(Kt,m,n,Kn)=O[nm+t+1/(logn)m+t]。

The upper bound of complete three-partite-graph Ramsey number r（kt,m,n,kn） is studied here.The set of large natural numbers is decomposed into {n′} and{n＂}.The lower bound of independence number is denoted by some gauss hypergeometric function.r（Kt,m,n,Kn）= O[n^m＋t＋1/（logn）^m＋t] is obtained.