Rui Zhang and Yongqi Sun and and Yali Wu The Bipartite Ramsey Numbers b(C2m; C2n)
152 - 155
2013
7
1
International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering http://waset.org/publications/15580
http://waset.org/publications/73
World Academy of Science, Engineering and Technology
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.
International Science Index 73, 2013