Tight codegree condition for the existence of loose hamilton cycles in 3-graphs

Andrzej Czygrinow; Theodore Molla

doi:10.1137/120890417

Tight codegree condition for the existence of loose hamilton cycles in 3-graphs

Andrzej Czygrinow, Theodore Molla

Mathematical and Statistical Sciences, School of (SoMSS)

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

21 Scopus citations

Abstract

In 2006, Kühn and Osthus [J. Combin. Theory Ser. B, 96 (2006), pp. 767 821] showed that if a 3-graph H on n vertices has minimum codegree at least (1/4 + o(1))n and n is even, then H has a loose Hamilton cycle. In this paper, we prove that the minimum codegree of n/4 suffices. The result is tight.

Original language	English (US)
Pages (from-to)	67-76
Number of pages	10
Journal	SIAM Journal on Discrete Mathematics
Volume	28
Issue number	1
DOIs	https://doi.org/10.1137/120890417
State	Published - 2014

Keywords

Absorbing lemma
Hamilton cycle
Hypergraphs

ASJC Scopus subject areas

Mathematics(all)

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10.1137/120890417

Cite this

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abstract = "In 2006, K{\"u}hn and Osthus [J. Combin. Theory Ser. B, 96 (2006), pp. 767 821] showed that if a 3-graph H on n vertices has minimum codegree at least (1/4 + o(1))n and n is even, then H has a loose Hamilton cycle. In this paper, we prove that the minimum codegree of n/4 suffices. The result is tight.",

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AU - Molla, Theodore

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AB - In 2006, Kühn and Osthus [J. Combin. Theory Ser. B, 96 (2006), pp. 767 821] showed that if a 3-graph H on n vertices has minimum codegree at least (1/4 + o(1))n and n is even, then H has a loose Hamilton cycle. In this paper, we prove that the minimum codegree of n/4 suffices. The result is tight.

KW - Absorbing lemma

KW - Hamilton cycle

KW - Hypergraphs

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Tight codegree condition for the existence of loose hamilton cycles in 3-graphs

Abstract

Keywords

ASJC Scopus subject areas

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