On the Ramsey Number $R(4,6)$

  • Geoffrey Exoo
Keywords: Ramsey number, edge coloring


The lower bound for the classical Ramsey number $R(4,6)$ is improved from 35 to 36. The author has found 37 new edge colorings of $K_{35}$ that have no complete graphs of order 4 in the first color, and no complete graphs of order 6 in the second color. The most symmetric of the colorings has an automorphism group of order 4, with one fixed point, and is presented in detail. The colorings were found using a heuristic search procedure.

Author Biography

Geoffrey Exoo, Indiana State University
Department of Mathematics and Computer Science
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