Colour-bias perfect matchings in hypergraphs

Hiêp Hàn; Richard Lang; João Pedro Marciano; Matías Pavez-Signé; Nicolás Sanhueza-Matamala; Andrew Treglown; Camila Zárate-Guerén

arXiv · 2408.11016

Colour-bias perfect matchings in hypergraphs

Hiêp Hàn·Richard Lang·João Pedro Marciano·Matías Pavez-Signé·Nicolás Sanhueza-Matamala·Andrew Treglown·Camila Zárate-Guerén

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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.

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Hiêp Hàn, Richard Lang, João Pedro Marciano, Matías Pavez-Signé, Nicolás Sanhueza-Matamala, Andrew Treglown, Camila Zárate-Guerén. 2025-06-30. Colour-bias perfect matchings in hypergraphs. https://arxiv.org/abs/2408.11016

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