Hamilton cycles in quasirandom hypergraphs

John Lenz; Dhruv Mubayi; Richard Mycroft

doi:10.1002/rsa.20638

Hamilton cycles in quasirandom hypergraphs

John Lenz, Dhruv Mubayi, Richard Mycroft

Mathematics

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

3 Citations (Scopus)

210 Downloads (Pure)

Abstract

We show that, for a natural notion of quasirandomness in k-uniform hypergraphs, any quasirandom k-uniform hypergraph on n vertices with constant edge density and minimum vertex degree Ω(nk-1) contains a loose Hamilton cycle. We also give a construction to show that a k-uniform hypergraph satisfying these conditions need not contain a Hamilton ℓ-cycle if k– ℓ divides k. The remaining values of ℓ form an interesting open question. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 2016

Original language	English
Journal	Random Structures and Algorithms
Early online date	26 Feb 2016
DOIs	https://doi.org/10.1002/rsa.20638
Publication status	E-pub ahead of print - 26 Feb 2016

Keywords

hypergraphs
Hamilton cycles
quasirandomness

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10.1002/rsa.20638Licence: None: All rights reserved

Hamilton cycles in quasirandom hypergraphs
This is the peer reviewed version of the following article: Hamilton cycles in quasirandom hypergraphs, which has been published in final form at 10.1002/rsa.20638. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.
Accepted author manuscript, 325 KBLicence: Other (please specify with Rights Statement)

Embeddings in hypergraphs
Mycroft, R. (Principal Investigator)
Engineering & Physical Science Research Council
30/03/15 → 29/03/17
Project: Research Councils

Cite this

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title = "Hamilton cycles in quasirandom hypergraphs",

abstract = "We show that, for a natural notion of quasirandomness in k-uniform hypergraphs, any quasirandom k-uniform hypergraph on n vertices with constant edge density and minimum vertex degree Ω(nk-1) contains a loose Hamilton cycle. We also give a construction to show that a k-uniform hypergraph satisfying these conditions need not contain a Hamilton ℓ-cycle if k– ℓ divides k. The remaining values of ℓ form an interesting open question. {\textcopyright} 2016 Wiley Periodicals, Inc. Random Struct. Alg., 2016",

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AU - Mycroft, Richard

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N2 - We show that, for a natural notion of quasirandomness in k-uniform hypergraphs, any quasirandom k-uniform hypergraph on n vertices with constant edge density and minimum vertex degree Ω(nk-1) contains a loose Hamilton cycle. We also give a construction to show that a k-uniform hypergraph satisfying these conditions need not contain a Hamilton ℓ-cycle if k– ℓ divides k. The remaining values of ℓ form an interesting open question. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 2016

AB - We show that, for a natural notion of quasirandomness in k-uniform hypergraphs, any quasirandom k-uniform hypergraph on n vertices with constant edge density and minimum vertex degree Ω(nk-1) contains a loose Hamilton cycle. We also give a construction to show that a k-uniform hypergraph satisfying these conditions need not contain a Hamilton ℓ-cycle if k– ℓ divides k. The remaining values of ℓ form an interesting open question. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 2016

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KW - Hamilton cycles

KW - quasirandomness

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DO - 10.1002/rsa.20638

M3 - Article

SN - 1042-9832

JO - Random Structures and Algorithms

JF - Random Structures and Algorithms

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Hamilton cycles in quasirandom hypergraphs

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