A Ramsey problem of Harary on graphs with prescribed size (Q1092061)

This paper contains several results relation the ``sizes'' of graphs and bounds on the corresponding Ramsey numbers. Two typical results: For any graph \(G\) with edges and no isolate vertices, \(r(K_3,G)\leq [8q/3]\). For a fixed graph \(G\) with \(p\) vertices (\(p\geq 3\)) and \(q\) edges, there exists a constant \(C\) such that for \(n\) sufficiently large, \(r(G,K_n)>C(n/\log(n))^{(p-1)(p-2)}\).