Computation of the Ramsey Number R(W5,K5)
Joshua Stinehour, Stanisław Radziszowski, Kung-Kuen Tse
Abstract
We determine the value of the Ramsey number R(W5,K5) to be 27, where W5 = K1 + C4 is the 4-spoked wheel of order 5. This solves one of the four remaining open cases in the tables given in 1989 by George R. T. Hendry, which included the Ramsey numbers R(G,H) for all pairs of graphs G and H having five vertices, except seven entries. In addition, we show that there exists a unique up to isomorphism critical Ramsey graph for W5 versus K5. Our results are based on computer algorithms.
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