University of Cambridge > Talks.cam > Combinatorics Seminar > Counting Hamiltonian cycles in Dirac hypergraphs

Counting Hamiltonian cycles in Dirac hypergraphs

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

  • UserAdva Mond (Cambridge)
  • ClockThursday 28 October 2021, 14:30-15:30
  • HouseMR12.

If you have a question about this talk, please contact ibl10.

For 0 ≤ r < k, a Hamiltonian r-cycle in a k-uniform hypergraph H is a cyclic ordering of the vertices of H in which the edges are segments of length k and every two consecutive edges overlap in exactly r vertices. We show that for all 0 ≤ r < k-1, every Dirac k-graph, that is, a k-graph with minimum co-degree pn for some p>1/2, has (up to a subexponential factor) at least as many Hamiltonian r-cycles as a typical random k-graph with edge-probability p. This improves a recent result of Glock, Gould, Joos, Osthus and Kühn, and verifies a conjecture of Ferber, Krivelevich and Sudakov for all values 0 ≤ r < k-1. (Joint work with Asaf Ferber and Liam Hardiman.)

This talk is part of the Combinatorics Seminar series.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.

 

© 2006-2022 Talks.cam, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity