Remarks on the size Ramsey number of graphs (Q1821796)

Let G denote a finite graph with vertex set V(G) and edge set E(G). If F is a second graph, we write \(G\to F\) to denote that, for every 2-coloring of the edges of G, G contains a monochromatic copy of F. The author defines: \(r(F)=\min \{| V(G)|: G\to F\},\) which one easily sees is the usual Ramsey number r(F,F). This formulation of the definition leads one to define the size Ramsey number: \(\hat r(F)=\min \{| E(G)|: G\to F\}.\) This paper contains several results concerning the size Ramsey number for special graphs. For example: \(\hat r(P_ 3)=7\), \(\hat r(P_ 4)\leq 11\); where \(P_ i\) is the path of length i.