In this paper we show that $e/n$ is the sharp threshold for the existence of
tight Hamilton cycles in random $k$-uniform hypergraphs, for all $k\ge 4$. When
$k=3$ we show that $1/n$ is an asymptotic threshold. We also determine
thresholds for the existence of other types of Hamilton cycles.Comment: 9 pages. Updated to add materia

Dudek, Andrzej

Frieze, Alan

SIAM Journal on Discrete Mathematics

English

arXiv

We say that a k-uniform hypergraph C is a Hamilton cycle of type l, for some 1 ≤ l ≤ k, if there exists a cyclic ordering of the vertices of C such that every edge consists of k consecutive vertices, and for every pair of consecutive edges E i-1\E i in C (in the natural ordering of the edges) we have |E i-1 \ E i| = l. We define a class of (ε, p)-regular hypergraphs, that includes random hypergraphs, for which we can prove the existence of a decomposition of almost all edges into type l Hamilton cycles, where l \u3c k/2

Bal, Deepak

Montclair State University Digital Commons

Packing Tight Hamilton Cycles in Uniform Hypergraphs

Andrzej Dudek

Alan Frieze

CiteSeerX

Tight Hamilton Cycles in Random Uniform Hypergraphs

Deepak Bal

Crossref

Tight Hamilton Cycles in Random Uniform Hypergraphs

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