Rainbow decompositions
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- by Raphael Yuster PDF
- Proc. Amer. Math. Soc. 136 (2008), 771-779 Request permission
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 \[ n \bmod k(k-1) \in \{1,k\},\] 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.References
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Additional Information
- Raphael Yuster
- Affiliation: Department of Mathematics, University of Haifa, Haifa 31905, Israel
- Email: raphy@math.haifa.ac.il
- Received by editor(s): September 28, 2006
- Published electronically: November 30, 2007
- Communicated by: Jim Haglund
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 771-779
- MSC (2000): Primary 05C15, 05C70, 05B40, 03E05
- DOI: https://doi.org/10.1090/S0002-9939-07-09204-0
- MathSciNet review: 2361848