Ramsey数r(mC_5,nC_5)

The Ramsey Number r(mC_5,nC_5)

对于图Ｇ和图Ｈ，Ｒａｍｓｅｙ 数ｒ（Ｇ，Ｈ） 定义最小正整数ｐ，使得经任意红、蓝２ 边着色的完全图Ｋｐ，或者其红色子图包含 Ｇ，或者其蓝色子图包含 Ｈ。以 ｍＣ５ 表示 ｍ 个互不相交的Ｃ５ 。可得：ｒ（ ｍＣ５ ，ｎＣ５） ＝５ｎ＋ ４， ｎ≥ｍ ＝ １３ ｍ ＋ ５ｎ －１ ， ｎ≥ｍ

If G and H graphs,the Ramsey number r(G,H) is defined to be the least number p such that if the edges of the complete graph K p are colored red and blue,either the red graph contains G as a subgraph or the blue graph contains H .Let m C 5 denote the union of m disjoint copies of C 5.In this paper,we prove that r(C 5,nC 5)=5n+4, n≥m=1 3m+5n-1, n≥m≥25n+4, n≥m=1 3m+5n-1, n≥m≥2.