Rainbow decompositions

Raphael Yuster

doi:10.1090/S0002-9939-07-09204-0

Rainbow decompositions

Raphael Yuster

Department of Mathematics

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

Abstract

A rainbow coloring of a graph is a coloring of the edges with distinct colors. We prove the following extension of Wilson's Theorem. For every integer k there exists an n₀ = n₀(k) so that for all n > n ₀, if n mod k(k - 1) ε {1, k}, then every properly edge-colored K_n contains (n/2)/(k/2) pairwise edge-disjoint rainbow copies of Kk. Our proof uses, as a main ingredient, a double application of the probabilistic method.

Original language	English
Pages (from-to)	771-779
Number of pages	9
Journal	Proceedings of the American Mathematical Society
Volume	136
Issue number	3
DOIs	https://doi.org/10.1090/S0002-9939-07-09204-0
State	Published - Mar 2008

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/S0002-9939-07-09204-0

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title = "Rainbow decompositions",

abstract = "A rainbow coloring of a graph is a coloring of the edges with distinct colors. We prove the following extension of Wilson's Theorem. For every integer k there exists an n0 = n0(k) so that for all n > n 0, if n mod k(k - 1) ε {1, k}, then every properly edge-colored Kn contains (n/2)/(k/2) pairwise edge-disjoint rainbow copies of Kk. Our proof uses, as a main ingredient, a double application of the probabilistic method.",

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AB - A rainbow coloring of a graph is a coloring of the edges with distinct colors. We prove the following extension of Wilson's Theorem. For every integer k there exists an n0 = n0(k) so that for all n > n 0, if n mod k(k - 1) ε {1, k}, then every properly edge-colored Kn contains (n/2)/(k/2) pairwise edge-disjoint rainbow copies of Kk. Our proof uses, as a main ingredient, a double application of the probabilistic method.

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Rainbow decompositions

Abstract

ASJC Scopus subject areas

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