Minimum codegree threshold for Hamilton l-cycles in k-uniform hypergraphs

Jie Han; Yi Zhao

doi:10.1016/j.jcta.2015.01.004

Minimum codegree threshold for Hamilton l-cycles in k-uniform hypergraphs

Jie Han
, Yi Zhao

Georgia State University
Department of Mathematics and Statistics

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

32 Citations (Scopus)

Abstract

For 1. ≤. ℓ. <. k/2, we show that for sufficiently large n, every k-uniform hypergraph on n vertices with minimum codegree at least n2(k-ℓ) contains a Hamilton ℓ-cycle. This codegree condition is best possible and improves on work of Hàn and Schacht who proved an asymptotic result.

Original language	English
Pages (from-to)	194-223
Number of pages	30
Journal	Journal of Combinatorial Theory. Series A
Volume	132
DOIs	https://doi.org/10.1016/j.jcta.2015.01.004
Publication status	Published - 1 May 2015
Externally published	Yes

Keywords

Absorbing method
Hamilton cycle
Hypergraph
Regularity lemma

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10.1016/j.jcta.2015.01.004

Cite this

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title = "Minimum codegree threshold for Hamilton l-cycles in k-uniform hypergraphs",

abstract = "For 1. ≤. ℓ. <. k/2, we show that for sufficiently large n, every k-uniform hypergraph on n vertices with minimum codegree at least n2(k-ℓ) contains a Hamilton ℓ-cycle. This codegree condition is best possible and improves on work of H{\`a}n and Schacht who proved an asymptotic result.",

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AU - Han, Jie

AU - Zhao, Yi

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N2 - For 1. ≤. ℓ. <. k/2, we show that for sufficiently large n, every k-uniform hypergraph on n vertices with minimum codegree at least n2(k-ℓ) contains a Hamilton ℓ-cycle. This codegree condition is best possible and improves on work of Hàn and Schacht who proved an asymptotic result.

AB - For 1. ≤. ℓ. <. k/2, we show that for sufficiently large n, every k-uniform hypergraph on n vertices with minimum codegree at least n2(k-ℓ) contains a Hamilton ℓ-cycle. This codegree condition is best possible and improves on work of Hàn and Schacht who proved an asymptotic result.

KW - Absorbing method

KW - Hamilton cycle

KW - Hypergraph

KW - Regularity lemma

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DO - 10.1016/j.jcta.2015.01.004

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VL - 132

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EP - 223

JO - Journal of Combinatorial Theory. Series A

JF - Journal of Combinatorial Theory. Series A

ER -

Minimum codegree threshold for Hamilton l-cycles in k-uniform hypergraphs

Abstract

Keywords

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