The Ramsey number for a cycle of length five vs. a complete graph of order six

Abstract

It has been conjectured that r(Cm, Kn) = (m − 1)(n − 1) + 1 for all m ≥ n ≥ 4. This has been proved recently for n = 4 and n = 5. In this paper, we prove that r(C5, K6) = 21. This raises the possibility that r(Cm, K6) = 5m − 4 for all m ≥ 5. © 2000 John Wiley & Sons, Inc. J Graph Theory 35: 99–108, 2000