A note on colour-bias perfect matchings in hypergraphs

Abstract

A result of Balogh, Csaba, Jing and Pluh\'ar yields the minimum degree threshold that ensures a $2$-coloured graph contains a perfect matching of significant colour-bias (i.e., a perfect matching that contains significantly more than half of its edges in one colour). In this note we prove an analogous result for perfect matchings in $k$-uniform hypergraphs. More precisely, for each $2\leq \ell <k$ and $r\geq 2$ we determine the minimum $\ell$-degree threshold for forcing a perfect matching of significant colour-bias in an $r$-coloured $k$-uniform hypergraph.