%0 Journal Article
%T Zarankiewicz Numbers and Bipartite Ramsey Numbers
%J Journal of Algorithms and Computation
%I University of Tehran
%Z 2476-2776
%A Collins, Alex F.
%A Riasanovsky, Alexander W. N.
%A Wallace, John C.
%A Radziszowski, Stanis law P.
%D 2016
%\ 06/10/2016
%V 47
%N 1
%P 63-78
%! Zarankiewicz Numbers and Bipartite Ramsey Numbers
%K Zarankiewicz number
%K bipartite Ramsey number
%R
%X The Zarankiewicz number z(b; s) is the maximum size of a subgraph of Kb,b which does not contain Ks,s as a subgraph. The two-color bipartite Ramsey number b(s, t) is the smallest integer b such that any coloring of the edges of Kb,b with two colors contains a Ks,s in the rst color or a Kt,t in the second color.In this work, we design and exploit a computational method for bounding and computing Zarankiewicz numbers. Using it, we obtain several new values and bounds on z(b; s) for 3≤s≤6. Our approach and new knowledge about z(b; s) permit us to improve some of the results on bipartite Ramsey numbers obtained by
%U https://jac.ut.ac.ir/article_7943_0d5d2a7f40f78dfe0e529df98f3049dd.pdf