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 ve 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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Center for Advancing the Study of CyberInfrastructure
S.P. Radziszowski, J. Stinehour, and K.K. Tse, "Note: Computation of the Ramsey Number R(W5K5). Bulletin of the Institute of Combinatorics and its Applications, 47 (2006) 53-57.
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