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Rainbow decompositions
Authors:Raphael Yuster
Institution:Department of Mathematics, University of Haifa, Haifa 31905, Israel
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 $ n_0=n_0(k)$ so that for all $ n > n_0$, if

$\displaystyle n \bmod k(k-1) \in \{1,k\},$

then every properly edge-colored $ K_n$ contains $ \binom{n}{2}/\binom{k}{2}$ pairwise edge-disjoint rainbow copies of $ K_k$.

Our proof uses, as a main ingredient, a double application of the probabilistic method.

Keywords:
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