Colour-bias perfect matchings in hypergraphs
Hi\^ep H\`an, Richard Lang, Jo\~ao Pedro Marciano, Mat\'ias Pavez-Sign\'e, Nicol\'as Sanhueza-Matamala, Andrew Treglown, Camila Z\'arate-Guer\'en
TL;DR
This paper investigates conditions for the existence of specific monochromatic perfect matchings in edge-coloured hypergraphs, providing solutions to open problems in the field under minimum degree constraints.
Contribution
It offers a new characterization of when hypergraphs contain monochromatic perfect matchings, addressing previously unresolved questions in hypergraph theory.
Findings
Established minimum degree conditions for perfect matchings in hypergraphs.
Solved open problems posed by Gishboliner, Glock, Sgueglia, Balogh, Treglown, and Zárate-Guerén.
Advances understanding of monochromatic structures in edge-coloured hypergraphs.
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.
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Taxonomy
Topicsgraph theory and CDMA systems · Graph Labeling and Dimension Problems · Advanced Graph Theory Research