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Monochromatic triangles in three-coloured graphs
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Cummings, James, Králʼ, Daniel, Pfender, Florian, Sperfeld, Konrad, Treglown, Andrew and Young, Michael (2013) Monochromatic triangles in three-coloured graphs. Journal of Combinatorial Theory, Series B, Volume 103 (Number 4). pp. 489-503. doi:10.1016/j.jctb.2013.05.002 ISSN 0095-8956.
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WRAP_Kral_1173667-ma-300613-monofinal.pdf - Accepted Version Download (456Kb) | Preview |
Official URL: http://dx.doi.org/10.1016/j.jctb.2013.05.002
Abstract
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.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Mathematics, Extremal problems (Mathematics), Graph theory, Graph coloring | ||||
Journal or Publication Title: | Journal of Combinatorial Theory, Series B | ||||
Publisher: | Academic Press | ||||
ISSN: | 0095-8956 | ||||
Official Date: | July 2013 | ||||
Dates: |
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Volume: | Volume 103 | ||||
Number: | Number 4 | ||||
Page Range: | pp. 489-503 | ||||
DOI: | 10.1016/j.jctb.2013.05.002 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Date of first compliant deposit: | 24 December 2015 | ||||
Date of first compliant Open Access: | 24 December 2015 | ||||
Funder: | National Science Foundation (U.S.) (NSF), Seventh Framework Programme (European Commission) (FP7), European Research Council (ERC) | ||||
Grant number: | DMS-1101156, DMS 0946431 (U.S.) (NSF) ; 259385 (ERC) |
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