TY - JOUR
T1 - Monochromatic triangles in three-coloured graphs
AU - Cummings, J.
AU - Král', D.
AU - Pfender, F.
AU - Sperfeld, K.
AU - Treglown, A.
AU - Young, M.
PY - 2013/7/1
Y1 - 2013/7/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84879788391&partnerID=8YFLogxK
U2 - 10.1016/j.jctb.2013.05.002
DO - 10.1016/j.jctb.2013.05.002
M3 - Article
AN - SCOPUS:84879788391
SN - 0095-8956
VL - 103
SP - 489
EP - 503
JO - Journal of Combinatorial Theory. Series B
JF - Journal of Combinatorial Theory. Series B
IS - 4
ER -