Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Thursday, February 23, 2017, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Penny Haxell (University of Waterloo)

Stability for matchings in regular hypergraphs

We consider a hypergraph analogue of the basic fact that every regular bipartite graph has a perfect matching. A theorem of Aharoni implies that every regular tripartite hypergraph $H$ with $n$ vertics in each class has a matching of size at least $n/2$, and moreover this bound is tight. We prove a stability version of this statement, showing that if $H$ has matching number close to $n/2$ then it is correspondingly close in structure to the extremal configuration.

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