In 1989, George R. T. Hendry presented a table of two-color graph Ramsey numbers R(G,H) for all pairs of graphs G and H having five vertices, with the exception of seven cases. Until now, only two of the these open cases were solved. This work eliminates another one by computing R(B_3,K_5) = 20, where B_3 = K_2 + K_3 is the book graph of order 5. In addition, we show that for these parameters there exists a unique up to isomorphism critical graph. The results are based on computer algorithms. Among the four remaining open cases in Hendry's table, the most notable is that of K_5 versus K_5, for which it is known that 43
Department, Program, or Center
Center for Advancing the Study of CyberInfrastructure
A. Babak, S.P. Radziszowski, and K.K. Tse, Computation of the Ramsey Number R(B_3,K_5). Bulletin of the Institute of Combinatorics and its Applications, 41 (2004), 71-76.
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