Maximum star deleted from Ramsey graphs of book and tree

Abstract

For graphs F, G and H, let F→(G,H) signify that any red/blue edge coloring of F contains a red G or a blue H. Define the Ramsey number R(G,H) to be the smallest r such that Kr→(G,H). In this note, we consider an optimization problem to find the star-critical Ramsey number RS(G,H) defined as max⁡{n|Kr∖K1,n→(G,H)} by showing that for n≥3m, RS(Bm,Tn)=n−2, where r=R(G,H).