Complete Critical Ramsey Numbers

Abstract:

For graphs G and H, Ramsey number r(G,H) is the smallest integer r such that every 2coloring of Kr contains either a red copy of G or a blue copy of H. Star critical Ramsey number r*(G,H) is the smallest integer n such that every 2coloring of KrK1,r-1-n contains either a red copy of G or a blue copy of H. Under the inspiration of star critical Ramsey number, complete critical Ramsey number rK(G,H) is the largest integer n such that every 2coloring of KrKn contains either a red copy of G or a blue copy of H. In this paper, rK(Wn,Ka) and rK(Cn,K3) are determined. Wn=K1+Cn-1 is a wheel of size n.