Minimum vertex degree threshold for loose Hamilton cycles in 3-uniform hypergraphs

Jie Han; Yi Zhao

doi:10.1016/j.jctb.2015.03.007

Minimum vertex degree threshold for loose Hamilton cycles in 3-uniform hypergraphs

Jie Han, Yi Zhao

Georgia State University

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

35 Citations (Scopus)

Abstract

We show that for sufficiently large n, every 3-uniform hypergraph on n vertices with minimum vertex degree at least (n-12)-(34n-2)+c, where c=. 2 if n∈4N and c=. 1 if n∈2N-4N, contains a loose Hamilton cycle. This degree condition is best possible and improves on the work of Buß, Hàn and Schacht who proved the corresponding asymptotical result.

Original language	English
Pages (from-to)	70-96
Number of pages	27
Journal	Journal of Combinatorial Theory. Series B
Volume	114
DOIs	https://doi.org/10.1016/j.jctb.2015.03.007
Publication status	Published - 1 Sept 2015
Externally published	Yes

Keywords

Absorbing method
Hamilton cycle
Hypergraph
Regularity lemma

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10.1016/j.jctb.2015.03.007

Cite this

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abstract = "We show that for sufficiently large n, every 3-uniform hypergraph on n vertices with minimum vertex degree at least (n-12)-(34n-2)+c, where c=. 2 if n∈4N and c=. 1 if n∈2N-4N, contains a loose Hamilton cycle. This degree condition is best possible and improves on the work of Bu{\ss}, H{\`a}n and Schacht who proved the corresponding asymptotical result.",

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AB - We show that for sufficiently large n, every 3-uniform hypergraph on n vertices with minimum vertex degree at least (n-12)-(34n-2)+c, where c=. 2 if n∈4N and c=. 1 if n∈2N-4N, contains a loose Hamilton cycle. This degree condition is best possible and improves on the work of Buß, Hàn and Schacht who proved the corresponding asymptotical result.

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KW - Hamilton cycle

KW - Hypergraph

KW - Regularity lemma

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ER -

Minimum vertex degree threshold for loose Hamilton cycles in 3-uniform hypergraphs

Abstract

Keywords

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