Asymptotic Size Ramsey Results for Bipartite Graphs

Details Asymptotic Size Ramsey Results for Bipartite Graphs Asymptotic Size Ramsey Results for Bipartite Graphs

2001-01-24

arxiv.org/abs/math/0101197v2

Mathematics

Combinatorics

14 pages + 3 pages of C code Submitted to SIAM Journal on Discrete Mathematics Version 2: the C code was rewritten to be used

Scientific paper

We investigate size Ramsey numbers involving bipartite graphs. It is proved that, if each forbidden graph is fixed or grows with n (in a certain uniform manner), then the extremal function has a linear asymptotics. The corresponding slope can be obtained as the minimum of a certain mixed integer program. Applying the Farkas Lemma, we solve the MIP for complete bipartite graphs, in particular answering a question of Erdos, Faudree, Rousseau and Schelp (1978) who asked for the asymptotics of the size Ramsey number of (K_{s,n},K_{s,n}) for fixed s and large n.

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