A Stability Theorem for Matchings in Tripartite 3-Graphs

Loading...
Thumbnail Image

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.

Description

Keywords

hypergraphs

LC Keywords

Citation