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Planar order on vertex poset

Funds:  Supported by the Fundamental Research Funds for the Central Universities.
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https://doi.org/10.3969/j.issn.0253-2778.2018.11.006
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  • Author Bio:

    LU Xuexing, male, born in 1984, PhD candidate. Research field: Mathematical physics. E-mail: xxlu@mail.ustc.edu.cn

  • Received Date: 23 October 2017
  • Accepted Date: 24 April 2018
  • Rev Recd Date: 24 April 2018
  • Publish Date: 30 November 2018
    Abstract

  • Abstract

    A planar order is a special linear extension of the edge poset (partially ordered set) of a processive plane graph. The definition of a planar order makes sense for any finite poset and is equivalent to the one of a conjugate order. Here it was proved that there is a planar order on the vertex poset of a processive planar graph naturally induced from the planar order of its edge poset.

    Abstract

    A planar order is a special linear extension of the edge poset (partially ordered set) of a processive plane graph. The definition of a planar order makes sense for any finite poset and is equivalent to the one of a conjugate order. Here it was proved that there is a planar order on the vertex poset of a processive planar graph naturally induced from the planar order of its edge poset.
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    • References(4)
  • [1]
    JOYAL A, STREET R. The geometry of tensor calculus,Ⅰ[J]. Adv Math, 1991, 88(1): 55-112.
    [2]
    HU S, LU X, YE Y. A graphical calculus approach to planar st graphs[EB/OL]. [2017-10-10] https://arxiv.org/abs/1604.07276.
    [3]
    DE FRAYSSEIX H, DE MENDEZ P O. Planarity and edge poset dimension[J]. European J Combin, 1996, 17(8): 731-740.
    [4]
    LU X, YE Y. Combinatorical characterization of upward planarity[EB/OL]. [2017-10-10] https://arxiv.org/abs/1608.07255.
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    [1]
    JOYAL A, STREET R. The geometry of tensor calculus,Ⅰ[J]. Adv Math, 1991, 88(1): 55-112.
    [2]
    HU S, LU X, YE Y. A graphical calculus approach to planar st graphs[EB/OL]. [2017-10-10] https://arxiv.org/abs/1604.07276.
    [3]
    DE FRAYSSEIX H, DE MENDEZ P O. Planarity and edge poset dimension[J]. European J Combin, 1996, 17(8): 731-740.
    [4]
    LU X, YE Y. Combinatorical characterization of upward planarity[EB/OL]. [2017-10-10] https://arxiv.org/abs/1608.07255.
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