A Stability Theorem for Matchings in Tripartite 3-Graphs
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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.
Cite this version of the work
Penny Haxell, Lothar Narins (2018). A Stability Theorem for Matchings in Tripartite 3-Graphs. UWSpace. http://hdl.handle.net/10012/16045