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On the existence of a rainbow 1-factor in 1-factorizations of K

✍ Scribed by S.I. El-Zanati; M.J. Plantholt; P.A. Sissokho; L.E. Spence

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
85 KB
Volume
15
Category
Article
ISSN
1063-8539

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✦ Synopsis

Abstract

Let ${\cal F}$ be a 1‐factorization of the complete uniform hypergraph ${\cal G}={K_{rn}^{(r)}}$ with $r \geq 2$ and $n\geq 3$. We show that there exists a 1‐factor of ${\cal G}$ whose edges belong to n different 1‐factors in ${\cal F}$. Such a 1‐factor is called a “rainbow” 1‐factor or an “orthogonal” 1‐factor. © 2007 Wiley Periodicals, Inc. J Combin Designs 15: 487–490, 2007

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