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

科研成果: 期刊稿件 › 文章 › 同行评审

36 引用（Scopus）

摘要

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.

源语言	英语
页（从-至）	70-96
页数	27
期刊	Journal of Combinatorial Theory. Series B
卷	114
DOI	https://doi.org/10.1016/j.jctb.2015.03.007
出版状态	已出版 - 1 9月 2015
已对外发布	是

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

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