Ramsey数r(mC_4,nC_4)

The Ramsey Number r(mC 4,nC 4)

对于图Ｇ和图Ｈ，Ｒａｍｓｅｙ数ｒ（Ｇ，Ｈ）定义为最小正整数ｐ，使得经任意红兰２边着色的完全图Ｋｐ，或者其红色子图包含Ｇ，或者其兰色子图包含Ｈ。以ｍＣ４表示ｍ个互不相交的Ｃ４。得到以下结论：当ｎ≥ｍ≥１，（ｍ，ｎ）≠（１，１）时，ｒ（ｍＣ４，ｎＣ４）＝２ｍ＋４ｎ－１。

If G and H are graphs,define the Ramsey number r(G,H) to be the least number p . 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 mC 4 denote the union of m disjoint copies of C 4 .In this paper,we prove that r(mC 4,nC 4)=2m+4n-1 ,where n≥m≥1,(m,n)≠(1,1).