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运筹学学报 ›› 2021, Vol. 25 ›› Issue (1): 123-131.doi: 10.15960/j.cnki.issn.1007-6093.2021.01.012

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最大边连通和super-边连通超图的充分条件

赵静1, 单而芳2, 赵加贵3,*()   

  1. 1. 上海大学数学系, 上海 200444
    2. 上海大学管理学院, 上海 200444
    3. 上海公安学院, 上海 200137
  • 收稿日期:2018-04-04 出版日期:2021-03-15 发布日期:2021-03-05
  • 通讯作者: 赵加贵 E-mail:416526575@qq.com
  • 作者简介:赵加贵 E-mail: 416526575@qq.com
  • 基金资助:
    国家自然科学基金(11971298)

Sufficient conditions for hypergraphs to be maximally edge-connected and super-edge-connected

Jing ZHAO1, Erfang SHAN2, Jiagui ZHAO3,*()   

  1. 1. Department of Mathematics, Shanghai University, Shanghai 200444, China
    2. School of Management, Shanghai University, Shanghai 200444, China
    3. Shanghai Police College, Shanghai 200137, China
  • Received:2018-04-04 Online:2021-03-15 Published:2021-03-05
  • Contact: Jiagui ZHAO E-mail:416526575@qq.com

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摘要：

设H是连通超图。若超图H的边连通度等于其最小度，则称H是最大边连通的。若超图H的每个最小边割总是由关联于某个最小度顶点的边集所构成，则称H是super-边连通的。首先给出一致线性超图是最大边连通超图的度序列条件。其次，给出一致线性超图是super-边连通超图的度条件。这些结果分别推广了Dankelmann和Volkmann（1997）以及Hellwig和Volkmann（2005）在图上的相关结论。

关键词: 超图, 边连通度, 最大边连通超图, super-边连通, 度序列最小度

Abstract:

Let H be a connected hypergraph. The hypergraph H is called maximally edge connected if its edge connectivity is equal to minimum degree. The hypergraph H is super-edge-connected, if every minimum edge-cut consists of edges adjacent to a vertex of minimum degree. In this paper we give simple degree sequence conditions for uniform linear hypergraphs to be maximally edge-connected. Also, we give a sufficient condition for uniform linear hypergraphs to be super-edge-connected. These results generalize previous results on graphs due to Dankelmann and Volkmann(1997), Hellwig and Volkmann(2005) to hypergraphs.

Key words: hypergraph, edge connectivity, maximally edgeconnected, degree sequence, super-edge-connected, minimum degree

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