A Stability Theorem for Matchings in Tripartite 3-Graphs
Loading...
Date
2018-04-02
Authors
Haxell, Penny
Narins, Lothar
Advisor
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.
Description
Keywords
hypergraphs