We provide new values of the bipartite Ramsey number R B ( C 4 , K 1 n ) using induced subgraphs incidence graph a projective plane. The approach, based on deleting subplanes planes, has been used in related extremal problems and allows us to unify previous results extend them. More importantly, deep stability 2 mod p sets double blocking sets, we can show some limits this technique when plane ...

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 H1 being even cycles a...