Loose Hamilton cycles in hypergraphs

Peter Keevash; Daniela Kuhn; Richard Mycroft; Deryk Osthus

doi:10.1016/j.disc.2010.11.013

Loose Hamilton cycles in hypergraphs

Peter Keevash, Daniela Kuhn, Richard Mycroft, Deryk Osthus

Mathematics

Research output: Contribution to journal › Article › peer-review

39 Citations (Scopus)

Abstract

We prove that any k-uniform hypergraph on n vertices with minimum degree at least n/2(k-1) + o(n) contains a loose Hamilton cycle. The proof strategy is similar to that used by Kuhn and Osthus for the 3-uniform case. Though some additional difficulties arise in the k-uniform case, our argument here is considerably simplified by applying the recent hypergraph blow-up lemma of Keevash. (C) 2010 Elsevier B.V. All rights reserved.

Original language	English
Pages (from-to)	544-559
Number of pages	16
Journal	Discrete Mathematics
Volume	311
Issue number	7
DOIs	https://doi.org/10.1016/j.disc.2010.11.013
Publication status	Published - 1 Apr 2011

Keywords

Hypergraph regularity
Blow-up lemma
Hamilton cycle
Hypergraph

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10.1016/j.disc.2010.11.013

Graph expansion and applications
Osthus, D.
Engineering & Physical Science Research Council
1/08/07 → 30/11/09
Project: Research Councils
Probabilistic Methods in Graph Theory
Kuhn, D. & Osthus, D.
Engineering & Physical Science Research Council
26/04/06 → 25/01/09
Project: Research Councils

Cite this

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title = "Loose Hamilton cycles in hypergraphs",

abstract = "We prove that any k-uniform hypergraph on n vertices with minimum degree at least n/2(k-1) + o(n) contains a loose Hamilton cycle. The proof strategy is similar to that used by Kuhn and Osthus for the 3-uniform case. Though some additional difficulties arise in the k-uniform case, our argument here is considerably simplified by applying the recent hypergraph blow-up lemma of Keevash. (C) 2010 Elsevier B.V. All rights reserved.",

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AU - Keevash, Peter

AU - Kuhn, Daniela

AU - Mycroft, Richard

AU - Osthus, Deryk

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Y1 - 2011/4/1

N2 - We prove that any k-uniform hypergraph on n vertices with minimum degree at least n/2(k-1) + o(n) contains a loose Hamilton cycle. The proof strategy is similar to that used by Kuhn and Osthus for the 3-uniform case. Though some additional difficulties arise in the k-uniform case, our argument here is considerably simplified by applying the recent hypergraph blow-up lemma of Keevash. (C) 2010 Elsevier B.V. All rights reserved.

AB - We prove that any k-uniform hypergraph on n vertices with minimum degree at least n/2(k-1) + o(n) contains a loose Hamilton cycle. The proof strategy is similar to that used by Kuhn and Osthus for the 3-uniform case. Though some additional difficulties arise in the k-uniform case, our argument here is considerably simplified by applying the recent hypergraph blow-up lemma of Keevash. (C) 2010 Elsevier B.V. All rights reserved.

KW - Hypergraph regularity

KW - Blow-up lemma

KW - Hamilton cycle

KW - Hypergraph

U2 - 10.1016/j.disc.2010.11.013

DO - 10.1016/j.disc.2010.11.013

M3 - Article

VL - 311

SP - 544

EP - 559

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 7

ER -

Loose Hamilton cycles in hypergraphs

Abstract

Keywords

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Projects

Graph expansion and applications

Probabilistic Methods in Graph Theory

Cite this