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Some Bipartite Ramsey Numbers

Authors:

Vites Longani

Affiliation:

(1) Dept. of Mathematics, Chiang Mai University, Thailand

Abstract:

Consider a complete bipartite graph K(s, s) with p = 2s points. Let each line of the graph have either red or blue colour. The smallest number p of points such that K(s, s) always contains red K(m, n) or blue K(m, n) is called bipartite Ramsey number denoted by rb(K(m, n), K(m, n)). In this paper, we show that

$r_{b}(K(1,n),(K(1,n))=4n-2(n=1,2,3ldots) r_{b}(K(2,2),(K(2,2))=10 r_{b}(K(2,3),(K(2,3))=18 r_{b}(K(3,3),(K(3,3))ge 30$

(2)

AMS Subject Classifications (1991): 05C15, 05D10.

Keywords:

bipartite Ramsey number bipartite graph

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