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Remarks on 15-vertex (3,3)-ramsey graphs not containing K₅

Sebastian Urbański — 1996

Discussiones Mathematicae Graph Theory

The paper gives an account of previous and recent attempts to determine the order of a smallest graph not containing K₅ and such that every 2-coloring of its edges results in a monochromatic triangle. A new 14-vertex K₄-free graph with the same Ramsey property in the vertex coloring case is found. This yields a new construction of one of the only two known 15-vertex (3,3)-Ramsey graphs not containing K₅.

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