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Monochromatic triangles in three colours

1988
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Bulletin of the Australian Mathematical Society
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Suppose the edges of the complete graph on 17 vertices are coloured in three colours. It is shown that at least five monochromatic triangles must arise. INTRODUCTION By a proper colouring of a graph G in n colours is meant a way of assigning n or fewer colours to the edges of G in such a way that no monochromatic triangle results. We are interested in edge-colourings of complete graphs. If K r denotes the complete graph on r vertices, then Ramsey's theorem guarantees the existence of a number r

doi:10.1017/s0004972700026733
fatcat:blz2eu325feh3ivcbam3pb64ja