Author:
Glock Stefan,Gould Stephen,Joos Felix,Kühn Daniela,Osthus Deryk
Abstract
AbstractA 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
$k\ge 3$
, 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
${\exp(n\ln n-\Theta(n))}$
. As a corollary, we obtain a similar estimate on the number of Hamilton
${\ell}$
-cycles in such k-graphs for all
${\ell\in\{0,\ldots,k-1\}}$
, which makes progress on a question of Ferber, Krivelevich and Sudakov.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Computational Theory and Mathematics,Statistics and Probability,Theoretical Computer Science
Cited by
1 articles.
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