The Ramsey number R(C4, Km) is the smallest n such that any graph on n vertices contains a cycle of length four or an independent set of order m. With the help of computer algorithms we obtain the exact values of the Ramsey numbers R(C4, K9) = 30 and R(C4, K10) = 36. New bounds for the next two open cases are also presented.
Department, Program, or Center
Computer Science (GCCIS)
Radziszowski, Stanislaw; Lange, Alexander; and Livinsky, Ivan, "Computation of the Ramsey Numbers R(C_4, K_9) and R(C_4, K_10)" (2016). Journal of Combinatorial Mathematics and Combinatorial Computing, 97 (), 139-154. Accessed from
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Available for download on Friday, July 12, 2019