Publication details
Monochromatic triangles in three-coloured graphs
| Authors | |
|---|---|
| Year of publication | 2013 |
| Type | Article in Periodical |
| Magazine / Source | JOURNAL OF COMBINATORIAL THEORY SERIES B |
| Citation | |
| Doi | http://dx.doi.org/10.1016/j.jctb.2013.05.002 |
| Keywords | Triangle density; Flag algebra; Extremal graph |
| Description | 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-n. Moreover, we characterise those 3-coloured copies of K-n that contain the minimum number of monochromatic triangles. (C) 2013 Elsevier Inc. All rights reserved. |