Colour-bias perfect matchings in hypergraphs

Andrew Treglown; Camila Z\'arate-Guer\'en; Hi\^ep H\`an; Jo\~ao Pedro Marciano; Mat\'ias Pavez-Sign\'e; Nicol\'as Sanhueza-Matamala; Richard Lang

Colour-bias perfect matchings in hypergraphs

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arxiv 2408.11016 v2 pith:FFUBUSH4 submitted 2024-08-20 math.CO

Hiêp Hàn , Richard Lang , João Pedro Marciano , Matías Pavez-Signé , Nicolás Sanhueza-Matamala , Andrew Treglown , Camila Zárate-Guerén This is my paper

classification math.CO

keywords conditionsmatchingsperfectunderanswersarate-guerbaloghcolour-bias

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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.

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Colour-biased Hamilton cycles in randomly perturbed graphs
math.CO 2025-06 reject novelty 7.0 of 10

Randomly perturbing a graph with O(n) random edges forces a colour-biased Hamilton cycle, and at the critical minimum degree the bias is proportional to m.

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