A NOTE ON COLOR-BIAS PERFECT HATCHINGS 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 <= & ell; < k and r >= 2 we determine the minimum & ell; -degree threshold for forcing a perfect matching of significant color-bias in an r-colored k-uniform hypergraph.