Colour-bias perfect matchings in hypergraphs
Combinatorics
2025-07-02 v2
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 Z\'arate-Guer\'en.
Cite
@article{arxiv.2408.11016,
title = {Colour-bias perfect matchings in hypergraphs},
author = {Hiêp Hàn and Richard Lang and João Pedro Marciano and Matías Pavez-Signé and Nicolás Sanhueza-Matamala and Andrew Treglown and Camila Zárate-Guerén},
journal= {arXiv preprint arXiv:2408.11016},
year = {2025}
}
Comments
22 pages, 1 figure. Author accepted manuscript, to appear in the SIAM Journal on Discrete Mathematics