DOI: 10.11908/j.issn.0253-374x.2019.02.020

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Complete Critical Ramsey Numbers
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Abstract:For graphs G and H, Ramsey number r(G,H) is the smallest integer r such that every 2ª²coloring 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 2ª²coloring of Krª²K1,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 2ª²coloring of Krª²Kn 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.





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