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A Stability Theorem for Matchings in Tripartite 3-Graphs

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Stability.pdf (352.42 KB)

Date

2018-04-02

Authors

Haxell, Penny
Narins, Lothar

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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

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Citation

URI

https://doi.org/10.1017/s0963548318000147
 http://hdl.handle.net/10012/16045

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Waterloo Research
Combinatorics and Optimization