10.5281/zenodo.1335404
https://zenodo.org/records/1335404
oai:zenodo.org:1335404
Rui Zhang
Rui Zhang
Yongqi Sun
Yongqi Sun
and Yali Wu
and Yali Wu
The Bipartite Ramsey Numbers b(C2m; C2n)
Zenodo
2013
2013-01-28
eng
10.5281/zenodo.1335403
15580
Creative Commons Attribution 4.0 International
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.