Colour-bias perfect matchings in hypergraphs.

Abstract: We study conditions under which an r-edge-coloured k-uniform hypergraph has a perfect matching that contains substantially more than n/(kr) monochromatic edges. Our main result solves this problem for perfect matchings under minimum degree conditions, which answers recent questions of Gishboliner, Glock and Sgueglia. This is joint work with Hiêp Hàn, Richard Lang, João Pedro Marciano, Matías Pavez-Signé, Andrew Treglown, and Camila Zárate-Guerén.