Perfect matchings in random sparsifications of Dirac hypergraphs

Add to your list(s) Download to your calendar using vCal

• Vincent Pfenniger, Birmingham
• Thursday 23 March 2023, 15:00-16:00
• Poynting 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.

This talk is included in these lists:

• Combinatorics and Probability seminar
• Poynting Small LT
• School of Mathematics events

Note that ex-directory lists are not shown.