Scholarly Research Excellence
%0 Journal Article
%A Rui Zhang and Yongqi Sun and and Yali Wu
%D 2013 
%J  International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering
%B World Academy of Science, Engineering and Technology
%I International Science Index 73, 2013
%T The Bipartite Ramsey Numbers b(C2m; C2n)
%U http://waset.org/publications/15580
%V 73
%X Given bipartite graphs H1 and H2, the bipartite Ramsey number b(H1;H2) is the smallest integer b such that any subgraph G of the complete bipartite graph Kb,b, either G contains a copy of H1 or its complement relative to Kb,b contains a copy of H2. It is known that b(K2,2;K2,2) = 5, b(K2,3;K2,3) = 9, b(K2,4;K2,4) = 14 and b(K3,3;K3,3) = 17. In this paper we study the case that both H1 and H2 are even cycles, prove that b(C2m;C2n) ≥ m + n - 1 for m = n, and b(C2m;C6) = m + 2 for m ≥ 4.

%P 152 - 155