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Edge-connectivity in hypergraphs

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Abstract

The edge-connectivity of a connected hypergraph H is the minimum number of edges (named as edge-cut) whose removal makes H disconnected. It is known that the edge-connectivity of a hypergraph is bounded above by its minimum degree. H is super edge-connected, if every edge-cut consists of edges incident with a vertex of minimum degree. A hypergraph H is linear if any two edges of H share at most one vertex. We call H uniform if all edges of H have the same cardinality. Sufficient conditions for equality of edge-connectivity and minimum degree of graphs and super edge-connected graphs are known. In this paper, we present a generalization of some of these sufficient conditions to linear and/or uniform hypergraphs.

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Authors and Affiliations

  1. College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046, China

    Shuang Zhao, Dan Li & Jixiang Meng

Authors
  1. Shuang Zhao
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  2. Dan Li
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  3. Jixiang Meng
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Corresponding author

Correspondence to Shuang Zhao.

Additional information

Communicated by Sharad S Sane.

The research is supported by NSFC (No. 11531011), XJTCDP (NO. 04231200746) and XJUDP (NO. 62031224601).

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Zhao, S., Li, D. & Meng, J. Edge-connectivity in hypergraphs. Indian J Pure Appl Math 52, 837–846 (2021). https://doi.org/10.1007/s13226-021-00052-5

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  • DOI: https://doi.org/10.1007/s13226-021-00052-5

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