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# Rainbow Decompositions

Raphael Yuster
Proceedings of the American Mathematical Society
Vol. 136, No. 3 (Mar., 2008), pp. 771-779
Stable URL: http://www.jstor.org/stable/20535235
Page Count: 9
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## 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 > n₀, if n mod k(k - 1) ∈ {1, k}, then every properly edge-colored $K_{n}$ contains $\left(\underset 2\to{n}\right)\diagup \left(\underset 2\to{k}\right)$ pairwise edge-disjoint rainbow copies of $K_{k}$. Our proof uses, as a main ingredient, a double application of the probabilistic method.

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