Monochromatic triangles in three-coloured graphs

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

doi:10.1016/j.jctb.2013.05.002

Monochromatic triangles in three-coloured graphs

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

Mathematics

Research output: Contribution to journal › Article › peer-review

18 Citations (Scopus)

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 K. Moreover, we characterise those 3-coloured copies of K that contain the minimum number of monochromatic triangles.

Original language	English
Pages (from-to)	489-503
Number of pages	15
Journal	Journal of Combinatorial Theory. Series B
Volume	103
Issue number	4
DOIs	https://doi.org/10.1016/j.jctb.2013.05.002
Publication status	Published - 1 Jul 2013

Access to Document

10.1016/j.jctb.2013.05.002

Cite this

@article{3c2f27154b174b5da117b8e1fd9fb324,

title = "Monochromatic triangles in three-coloured graphs",

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 K. Moreover, we characterise those 3-coloured copies of K that contain the minimum number of monochromatic triangles.",

author = "J. Cummings and D. Kr{\'a}l' and F. Pfender and K. Sperfeld and A. Treglown and M. Young",

year = "2013",

month = jul,

day = "1",

doi = "10.1016/j.jctb.2013.05.002",

language = "English",

volume = "103",

pages = "489--503",

journal = "Journal of Combinatorial Theory. Series B",

issn = "0095-8956",

publisher = "Elsevier",

number = "4",

}

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 - https://www.scopus.com/pages/publications/84879788391

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 -

Monochromatic triangles in three-coloured graphs

Abstract

Access to Document

Fingerprint

Cite this