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arXiv · 1206.1987

Monochromatic triangles in three-coloured graphs

James Cummings·Daniel Král'·Florian Pfender·Konrad Sperfeld·Andrew Treglown·Michael Young
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Abstract

In 1959, Goodman determined the minimum number of monochromatic triangles in a complete graph whose edge set is two-coloured. Goodman also raised the question of proving analogous results for complete graphs whose edge sets are coloured with more than two colours. In this paper, we determine the minimum number of monochromatic triangles and the colourings which achieve this minimum in a sufficiently large three-coloured complete graph.

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James Cummings, Daniel Král', Florian Pfender, Konrad Sperfeld, Andrew Treglown, Michael Young. 2012-06-10. Monochromatic triangles in three-coloured graphs. https://arxiv.org/abs/1206.1987

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