Abstract

For graphs F, G and H, let F→(G,H) signify that any red/blue edge coloring of F contains either a red G or a blue H. The Ramsey number R(G,H) is defined as min⁡{r|Kr→(G,H)}. In this note, we consider an optimization problem to bound the complete bipartite-critical Ramsey number RΛ(G,H) defined as max⁡{t|Kr∖Kt,t→(G,H)} where r=R(G,H) and Λ is a set of Kt,t, and determine RΛ(G,H) for some pairs (G,H).

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