A new upper bound for the Ramsey number R(5,5)

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Title: A new upper bound for the Ramsey number R(5,5)
Author: McKay, Brendan; Radziszowski, Stanislaw
Abstract: We show that, in any colouring of the edges of K_53 with two colours, there exists a monochromatic K_5, and hence R(5,5) <= 53. This is accomplished in three stages: a full enumeration of edges in (4,5)-good graphs, and a proof of the nonexistence of (5,5)-good graphs on 53 vertices. Only the first stage required extensive help from the computer.
Description: This article is also available at the publisher's website at: http://ajc.maths.uq.edu.au/
Record URI: http://hdl.handle.net/1850/8009
Date: 1992

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