The planar Ramsey number I

The planar Ramsey number PR(H1, H2) is the smallest integer n such that any planar graph on n vertices contains a copy of H1 or its complement contains a copy of H2. It is known that the Ramsey number R(C4, K7) = 22. The planar Ramsey numbers PR(C4, Kl ) for l ≤ 6 are known. In this paper we show that PR(C4, K7) = 20. c © 2008 Published by Elsevier B.V.

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