Counting Hamiltonian cycles in Dirac hypergraphs

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• Adva Mond (Cambridge)
• Thursday 28 October 2021, 14:30-15:30
• MR12.

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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.

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