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CATEGORIES:Combinatorics Seminar
SUMMARY:Counting Hamiltonian cycles in Dirac hypergraphs -
  Adva Mond (Cambridge)
DTSTART;TZID=Europe/London:20211028T143000
DTEND;TZID=Europe/London:20211028T153000
UID:TALK165034AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/165034
DESCRIPTION:For 0 ≤ r < k\, a Hamiltonian r-cycle in a k-unifo
 rm hypergraph H is a cyclic ordering of the vertic
 es of H in which the edges are segments of length 
 k and every two consecutive edges overlap in exact
 ly r vertices.\nWe show that for all 0 ≤ r < k-1\,
  every Dirac k-graph\, that is\, a k-graph with mi
 nimum co-degree pn for some p>1/2\, has (up to a s
 ubexponential factor) at least as many Hamiltonian
  r-cycles as a typical random k-graph with edge-pr
 obability p.\nThis improves a recent result of Glo
 ck\, 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 Asaf
  Ferber and Liam Hardiman.)\n
LOCATION:MR12
CONTACT:
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