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SUMMARY:Counting Hamiltonian cycles in Dirac hypergraphs - Adva Mond (Camb
 ridge)
DTSTART:20211028T133000Z
DTEND:20211028T143000Z
UID:TALK165034@talks.cam.ac.uk
CONTACT:103978
DESCRIPTION:For 0 ≤ r < k\, a Hamiltonian r-cycle in a k-uniform hypergr
 aph H is a cyclic ordering of the vertices of H in which the edges are seg
 ments of length k and every two consecutive edges overlap in exactly r ver
 tices.\nWe 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 subex
 ponential factor) at least as many Hamiltonian r-cycles as a typical rando
 m k-graph with edge-probability p.\nThis 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.\n(Joint work with A
 saf Ferber and Liam Hardiman.)\n
LOCATION:MR12
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