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A Stability Theorem for Matchings in Tripartite 3-Graphs

Published online by Cambridge University Press:  02 April 2018

PENNY HAXELL
Affiliation:
Combinatorics and Optimization Department, University of Waterloo, Waterloo, ON, CanadaN2L 3G1 (e-mail: pehaxell@uwaterloo.ca)
LOTHAR NARINS
Affiliation:
Combinatorics and Optimization Department, University of Waterloo, Waterloo, ON, CanadaN2L 3G1 (e-mail: pehaxell@uwaterloo.ca)
Corresponding
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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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Copyright © Cambridge University Press 2018 

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Footnotes

Partially supported by NSERC. This author also thanks the Mittag-Leffler Institute in Djursholm, Sweden, where part of this work was done.

References

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