The Number of Edge Colorings with No Monochromatic Triangle

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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.

Original languageEnglish
Pages (from-to)441-452
Number of pages12
JournalJournal of Graph Theory
Issue number4
StatePublished - Apr 1996
Externally publishedYes

ASJC Scopus subject areas

  • Geometry and Topology


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