Monochromatic triangles in three-coloured graphs

J. Cummings, D. Král', F. Pfender, K. Sperfeld, A. Treglown, M. Young

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)


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 K. Moreover, we characterise those 3-coloured copies of K that contain the minimum number of monochromatic triangles.
Original languageEnglish
Pages (from-to)489-503
Number of pages15
JournalJournal of Combinatorial Theory. Series B
Issue number4
Publication statusPublished - 1 Jul 2013


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