Monochromatic triangles in three-coloured graphs

CUMMINGS, J; Daniel KRÁĽ; F PFENDER; K SPERFELD; A TREGLOWN a M YOUNG. Monochromatic triangles in three-coloured graphs. JOURNAL OF COMBINATORIAL THEORY SERIES B. SAN DIEGO: ACADEMIC PRESS INC ELSEVIER SCIENCE, 2013, roč. 103, č. 4, s. 489-503. ISSN 0095-8956. Dostupné z: https://doi.org/10.1016/j.jctb.2013.05.002.

Základní údaje

Originální název

Monochromatic triangles in three-coloured graphs

Autoři

CUMMINGS, J; Daniel KRÁĽ; F PFENDER; K SPERFELD; A TREGLOWN a M YOUNG

Vydání

JOURNAL OF COMBINATORIAL THEORY SERIES B, SAN DIEGO, ACADEMIC PRESS INC ELSEVIER SCIENCE, 2013, 0095-8956

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Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Utajení

není předmětem státního či obchodního tajemství

Impakt faktor

Impact factor: 0.939

DOI

https://doi.org/10.1016/j.jctb.2013.05.002

UT WoS

000321725600005

Klíčová slova anglicky

Triangle density; Flag algebra; Extremal graph

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Anotace

V originále

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.