A Stability Theorem for Matchings in Tripartite 3-Graphs
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Date
2018-04-02
Authors
Haxell, Penny
Narins, Lothar
Journal Title
Journal ISSN
Volume Title
Publisher
Cambridge University Press
Abstract
It follows from known results that every regular tripartite hypergraph of positive degree, with n vertices in each class, has matching number at least n/2. This bound is best possible, and the extremal configuration is unique. Here we prove a stability version of this statement, establishing that every regular tripartite hypergraph with matching number at most (1 + ϵ)n/2 is close in structure to the extremal configuration, where ‘closeness’ is measured by an explicit function of ϵ.
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Keywords
hypergraphs