On the existence of a rainbow 1-factor in proper coloring of K_{rn}^{(r)}

Abstract

El-Zanati et al proved that for any 1-factorization $\mathcal{F}$ of the complete uniform hypergraph $\mathcal{G}=K_{rn}^{(r)}$ with $r\ge 2$ and $n\ge 3$, there is a rainbow 1-factor. We generalize their result and show that in any proper coloring of the complete uniform hypergraph $\mathcal{G}=K_{rn}^{(r)}$ with $r\ge 2$ and $n\ge 3$, there is a rainbow 1-factor.

6 pages