A Note on Color-Bias Perfect Matchings in Hypergraphs

A result of Balogh et al. yields the minimum degree threshold that ensures a 2- colored graph contains a perfect matching of significant color-bias (i.e., a perfect matching that contains significantly more than half of its edges in one color). In this note we prove an analogous result for perfect matchings in k-uniform hypergraphs. More precisely, for each 2 ≤ ℓ < k and r ≥ 2 we determine the minimum ℓ-degree threshold for forcing a perfect matching of significant color-bias in an r-colored k-uniform hypergraph.