关于路和圈的3-色Ramsey数

On Some Three-color Ramsey Numbers of Paths and Cycles

摘要:

对于给定的图G1，G2，…，Gk ,k≥2，k-色Ramsey数R（G1，G2，…，Gk）是指最小的正整数n，使得对n个点的完全图进行任意的k-边染色，总是存在某个染i色的单色图Gi，1≤i≤k.对G1 =G2= Pm，G3= Cn的情况进行了研究，得到了n较大时的3-色Ramsey数R(Pm , Pm,Cn)的准确值.

关键词:路; 圈; 3-色 Ramsey数

Abstract:

For given graphs G1,G2,…,Gk, where k≥2, the k-color Ramsey number R（G1, G2,…, Gk）is the smallest integer n such that if we arbitrarily color the edges of the complete graph on n vertices with k colors, there is always a monochromatic copy of Gi colored with color i, for some 1≤i≤k. In this note, we provide the exact value for 3color Ramsey R(Pm , Pm,Cn), where n is larger than m.

Key words:path; cycle; 3-color Ramsey number