Colour-bias perfect matchings in hypergraphs
arXiv:2408.11016
Abstract
We study conditions under which an edge-coloured hypergraph has a particular substructure that contains more than the trivially guaranteed number of monochromatic edges. Our main result solves this problem for perfect matchings under minimum degree conditions. This answers recent questions of Gishboliner, Glock and Sgueglia, and of Balogh, Treglown and Zárate-Guerén.
22 pages, 1 figure. Author accepted manuscript, to appear in the SIAM Journal on Discrete Mathematics