The Number of Edge Colorings with No Monochromatic Triangle

Raphael Yuster

doi:10.1002/(SICI)1097-0118(199604)21:4<441::AID-JGT10>3.0.CO;2-I

The Number of Edge Colorings with No Monochromatic Triangle

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Abstract

Let F(n, k) denote the maximum number of two edge colorings of a graph on n vertices that admit no monochromatic K_k, (a complete graph on k vertices). The following results are proved: F(n, 3) = 2^[n2/4] for all n ≥ 6. F(n, k) = 2^{((k-2)/(2k-2)+o(1))n2}. In particular, the first result solves a conjecture of Erdös and Rothschild.

Original language	English
Pages (from-to)	441-452
Number of pages	12
Journal	Journal of Graph Theory
Volume	21
Issue number	4
DOIs	https://doi.org/10.1002/(SICI)1097-0118(199604)21:4<441::AID-JGT10>3.0.CO;2-I
State	Published - Apr 1996
Externally published	Yes

ASJC Scopus subject areas

Geometry and Topology

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10.1002/(SICI)1097-0118(199604)21:4<441::AID-JGT10>3.0.CO;2-I

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title = "The Number of Edge Colorings with No Monochromatic Triangle",

abstract = "Let F(n, k) denote the maximum number of two edge colorings of a graph on n vertices that admit no monochromatic Kk, (a complete graph on k vertices). The following results are proved: F(n, 3) = 2[n2/4] for all n ≥ 6. F(n, k) = 2((k-2)/(2k-2)+o(1))n2. In particular, the first result solves a conjecture of Erd{\"o}s and Rothschild.",

author = "Raphael Yuster",

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AB - Let F(n, k) denote the maximum number of two edge colorings of a graph on n vertices that admit no monochromatic Kk, (a complete graph on k vertices). The following results are proved: F(n, 3) = 2[n2/4] for all n ≥ 6. F(n, k) = 2((k-2)/(2k-2)+o(1))n2. In particular, the first result solves a conjecture of Erdös and Rothschild.

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The Number of Edge Colorings with No Monochromatic Triangle

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