Three Early Problems on Size Ramsey Numbers

The size Ramsey number of a graph H is defined as the minimum edges in G such that there monochromatic copy every two-coloring E(G). was introduced by Erdős, Faudree, Rousseau, and Schelp 1978 they ended their foundational paper asking whether one can determine up to constant factor numbers three families graphs: complete bipartite graphs, book graphs (obtained adding many common neighbors vertices clique), starburst pendant each vertex clique). In this paper, we completely resolve latter two questions make substantial progress on first determining $$K_{s,t}$$ for all $$t =\Omega (s\log s)$$ .