University of Birmingham > Talks@bham > Combinatorics and Probability seminar > Perfect matchings in random sparsifications of Dirac hypergraphs

Perfect matchings in random sparsifications of Dirac hypergraphs

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  • UserVincent Pfenniger, Birmingham
  • ClockThursday 23 March 2023, 15:00-16:00
  • HousePoynting Small LT.

If you have a question about this talk, please contact Dr Richard Mycroft.

We show that, for k >= 3 and n divisible by k, if a k-uniform hypergraph H on n vertices has large enough minimum (k-1)-degree to guarantee a perfect matching, then asymptotically almost surely a p-random subhypergraph of H also contains a perfect matching, provided that p > C log n / n^{k-1}. Our result strengthens Johansson, Kahn, and Vu’s seminal solution to Shamir’s problem and can be viewed as a ‘robust’ version of a hypergraph Dirac-type result by Rödl, Ruciński, and Szemerédi.

This talk is part of the Combinatorics and Probability seminar series.

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