An approximate ore-type result for tight Hamilton cycles in uniform hypergraphs

Tang, Yucong; Yan, Guangwu

doi:10.1016/j.disc.2017.02.018

Cited by 6 publications

(2 citation statements)

References 8 publications

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“…Motivated by the relation between Dirac's condition and Ore's condition for Hamilton cycles, Tang and Yan [18] studied the degree sum of two (k − 1)-sets that guarantees a tight Hamilton cycle in k-graphs. Zhang and Lu [22] studied the degree sum of two (k − 1)-sets that guarantees a perfect matching in kuniform hypergraphs.…”

Section: Introductionmentioning

confidence: 99%

Vertex Degree Sums for Perfect Matchings in 3-Uniform Hypergraphs

Zhang

Zhao

2018

Electron. J. Combin.

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We determine the minimum degree sum of two adjacent vertices that ensures a perfect matching in a 3-graph without isolated vertex. More precisely, suppose that H is a 3-uniform hypergraph whose order n is sufficiently large and divisible by 3. If H contains no isolated vertex and deg(u)+ deg(v) > 2 3 n 2 − 8 3 n + 2 for any two vertices u and v that are contained in some edge of H, then H contains a perfect matching. This bound is tight.

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Section: Introductionmentioning

confidence: 99%

Vertex Degree Sums for Perfect Matchings in 3-Uniform Hypergraphs

Zhang

Zhao

2018

Electron. J. Combin.

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“…Ore-type problems for hypergraphs have been studied recently. For example, Tang and Yan [19] studied the degree sum of two (k − 1)-sets that guarantees a tight Hamilton cycle in k-graphs. Zhang and Lu [23] studied the degree sum of two (k − 1)-sets that guarantees a perfect matching in k-graphs.…”

Section: Introductionmentioning

confidence: 99%

Vertex Degree Sums for Matchings in 3-Uniform Hypergraphs

Zhang

Zhao

2019

Electron. J. Combin.

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Let n, s be positive integers such that n is sufficiently large and s ≤ n/3. Suppose H is a 3-uniform hypergraph of order n. If H contains no isolated vertex and deg(u) + deg(v) > 2(s − 1)(n − 1) for any two vertices u and v that are contained in some edge of H, then H contains a matching of size s. This degree sum condition is best possible and confirms a conjecture of the authors [Electron. J. Combin. 25 (3), 2018], who proved the case when s = n/3. n−1 2 − n−s 2 and n ≥ 3s, then H contains a matching of size s.

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Some Ore-type Results for Matching and Perfect Matching in k-uniform Hypergraphs

Zhang

2018

Acta. Math. Sin.-English Ser.

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An approximate ore-type result for tight Hamilton cycles in uniform hypergraphs

Cited by 6 publications

References 8 publications

Vertex Degree Sums for Perfect Matchings in 3-Uniform Hypergraphs

Vertex Degree Sums for Perfect Matchings in 3-Uniform Hypergraphs

Vertex Degree Sums for Matchings in 3-Uniform Hypergraphs

Some Ore-type Results for Matching and Perfect Matching in k-uniform Hypergraphs

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