University of Birmingham > Talks@bham > Combinatorics and Probability Seminar > Counting Hamilton cycles in Dirac hypergraphs

Counting Hamilton cycles in Dirac hypergraphs

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  • UserStephen Gould (University of Birmingham)
  • ClockThursday 06 February 2020, 15:00-16:00
  • HouseWatson LTA.

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

A tight Hamilton cycle in a k-uniform hypergraph (k-graph) G is a cyclic ordering of the vertices of G such that every set of k consecutive vertices in the ordering forms an edge. Rödl, Ruciński, and Szemerédi proved that for k≥3, every k-graph on n vertices with minimum codegree at least n/2+o(n) contains a tight Hamilton cycle. We show that the number of tight Hamilton cycles in such k-graphs is exp(n ln n − Θ(n)). As a corollary, we obtain a similar estimate on the number of Hamilton l-cycles in such k-graphs for all l∈{0,…,k−1}, which addresses a question of Ferber, Krivelevich and Sudakov.

This is joint work with Stefan Glock, Felix Joos, Daniela Kühn, and Deryk Osthus.

This talk is part of the Combinatorics and Probability Seminar series.

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