Bipartite Ramsey numbers involving large Kn,n

Authors:
Qizhong Lin;Yusheng Li
Affiliations:
Department of Mathematics, Tongji University, Shanghai 200092, China;Department of Mathematics, Tongji University, Shanghai 200092, China
Venue:
European Journal of Combinatorics
Year:
2009

Citing 2
Cited 0

Ramsey numbers involving large dense graphs and bipartite Turán numbers

Journal of Combinatorial Theory Series B
Turán Numbers of Bipartite Graphs and Related Ramsey-Type Questions

Combinatorics, Probability and Computing

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Abstract

Let br(H1,H2) be the bipartite Ramsey number for bipartite graphs H1 and H2. It is shown that the order of magnitude of br(Kt,n,Kn,n) is nt+1/(logn)t for t≥1 fixed and n→∞. Moreover, if H is an isolate-free bipartite graph of order h having bipartition (A,B) that satisfies Δ(B)≤t, then br(H,Kn,n) can be bounded from above by (hn/logn)t(logn)α( t) for large n, where α(1)=α(2)=1 and α(t)=0 for t≥3.