Matchings in balanced hypergraphs
Robert Scheidweiler, Eberhard Triesch
TL;DR
This paper presents new proofs and generalizations of classical matching theorems to balanced hypergraphs, offering novel characterizations and insights into their matching and vertex cover properties.
Contribution
It provides a new proof of K"onig's theorem and extends the Gallai-Edmonds decomposition to balanced hypergraphs with two different approaches.
Findings
New characterizations of balanced hypergraphs
Generalized Gallai-Edmonds decomposition
Properties of matchings and vertex covers in balanced hypergraphs
Abstract
We give a new proof of K\"onig's theorem and generalize the Gallai-Edmonds decomposition to balanced hypergraphs in two different ways. Based on our decompositions we give two new characterizations of balanced hypergraphs and show some properties of matchings and vertex cover in balanced hypergraphs.
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph theory and applications · Limits and Structures in Graph Theory