Multicolor Bipartite Ramsey Number of C-4 and Large Kn,n

作者：Lin, Qizhong^*; Li, Yusheng

来源：Journal of Graph Theory, 2011, 67(1): 47-54.

DOI：10.1002/jgt.20512

• bipartite Ramsey number
• cycle
• asymptotic bound

Let br(k) (C-4; K-n,K-n) be the smallest N such that if all edges of K-N,K-N are colored by k + 1 colors, then there is a monochromatic C-4 in one of the first k colors or a monochromatic Kn, n in the last color. It is shown that brk (C-4; K-n,K-n) = Theta(n(2)/log(2)n) for k >= 3, and br(2)(C-4; K-n,K-n) >= c(n log logn/log(2) n)(2) for large n. The main part of the proof is an algorithm to bound the number of large K-n,K-n in quasi-random graphs.

• 出版日期2011-5
• 单位同济大学; 福州大学