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Ore-type condition for loose Hamilton cycles in 3-uniform hypergraphs

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https://doi.org/10.3969/j.issn.0253-2778.2020.05.014
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  • Author Bio:

    YU Lei, male, born in 1990,PhD.Research field: Geometry and analysis.

  • Received Date: 08 June 2019
  • Accepted Date: 15 October 2019
  • Rev Recd Date: 15 October 2019
  • Publish Date: 31 May 2020
    Abstract

  • Abstract

    A classic result of Ore in 1960 states that if the degree sum of any two independent vertices in an n-vertex graph is at least n, then the graph is Hamiltonian. Here a similar problem for 3-uniform hypergraph was studied and an approximate result was obtained.

    Abstract

    A classic result of Ore in 1960 states that if the degree sum of any two independent vertices in an n-vertex graph is at least n, then the graph is Hamiltonian. Here a similar problem for 3-uniform hypergraph was studied and an approximate result was obtained.
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    • References(4)
  • [1]
    ORE O. A note on Hamiltonian circuits[J]. Amer. Math Monthly, 1960, 67: 55.
    [2]
    TANG Y, YAN G. An approximate Ore-type result for tight Hamilton cycles in uniform hypergraphs[J]. Discrete Math, 2017, 340: 1528-1534.
    [3]
    CZYGRINOW A, MOLLA T. Tight codegree condition for the existence of loose Hamilton cycles in 3-graphs[J]. SIAM J. Discrete Math, 2014, 28(1): 67-76.
    [4]
    HN H, SCHACHT M. Dirac-type results for loose Hamilton cycles in uniform hypergraphs[J]. J.Comb. Theory Ser. B, 2010, 100: 332-346.)
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    [1]
    ORE O. A note on Hamiltonian circuits[J]. Amer. Math Monthly, 1960, 67: 55.
    [2]
    TANG Y, YAN G. An approximate Ore-type result for tight Hamilton cycles in uniform hypergraphs[J]. Discrete Math, 2017, 340: 1528-1534.
    [3]
    CZYGRINOW A, MOLLA T. Tight codegree condition for the existence of loose Hamilton cycles in 3-graphs[J]. SIAM J. Discrete Math, 2014, 28(1): 67-76.
    [4]
    HN H, SCHACHT M. Dirac-type results for loose Hamilton cycles in uniform hypergraphs[J]. J.Comb. Theory Ser. B, 2010, 100: 332-346.)
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