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

## Counting Hamiltonian cycles in Dirac hypergraphsAdd to your list(s) Download to your calendar using vCal - Adva Mond (Cambridge)
- Thursday 28 October 2021, 14:30-15:30
- MR12.
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. ## This talk is included in these lists:- All CMS events
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