Monochromatic triangles in three-coloured graphs
Combinatorics
2012-06-12 v1
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.
Cite
@article{arxiv.1206.1987,
title = {Monochromatic triangles in three-coloured graphs},
author = {James Cummings and Daniel Král' and Florian Pfender and Konrad Sperfeld and Andrew Treglown and Michael Young},
journal= {arXiv preprint arXiv:1206.1987},
year = {2012}
}
Comments
Some data needed to verify the proof can be found at http://www.math.cmu.edu/users/jcumming/ckpsty/