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Monochromatic triangles in three-coloured graphs

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posted on 2012-06-01, 00:00 authored by James CummingsJames Cummings, Daniel Kral, Florian Pfender, Konrad Sperfeld, Andrew Treglown

In 1959, Goodman [9] determined the minimum number of monochromatic triangles in a complete graph whose edge set is 2-coloured. Goodman (1985) [10] also raised the question of proving analogous results for complete graphs whose edge sets are coloured with more than two colours. In this paper, for n sufficiently large, we determine the minimum number of monochromatic triangles in a 3-coloured copy of Kn. Moreover, we characterise those 3-coloured copies of Kn that contain the minimum number of monochromatic triangles.

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This is the author’s version of a work that was accepted for publication. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version is available at http://dx.doi.org/10.1016/j.jctb.2013.05.002

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2012-06-01

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