2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60809We 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.14 pages + 3 pages of C code Submitted to SIAM Journal on Discrete Mathematics Version 2: the C code was rewritten to be used with the lrslib libraryCombinatorics05C55text