TL;DR
This paper surveys the perfect matching problem in hypergraphs, focusing on structural conditions for existence in dense hypergraphs and the existence of combinatorial designs.
Contribution
It provides a comprehensive overview of structural characterisations and existence results for perfect matchings and designs in hypergraphs.
Findings
Structural characterisations of perfect matchings in dense hypergraphs
Existence criteria for combinatorial designs in hypergraphs
Overview of recent advances in hypergraph matching theory
Abstract
We survey some aspects of the perfect matching problem in hypergraphs, with particular emphasis on structural characterisation of the existence problem in dense hypergraphs and the existence of designs.
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