The edge‐connectivity of vertex‐transitive hypergraphs

Author:

Burgess Andrea C.1,Luther Robert D.2ORCID,Pike David A.2

Affiliation:

1. Department of Mathematics and Statistics University of New Brunswick Saint John New Brunswick Canada

2. Department of Mathematics and Statistics Memorial University of Newfoundland St. John's Newfoundland Canada

Abstract

AbstractA graph or hypergraph is said to be vertex‐transitive if its automorphism group acts transitively upon its vertices. A classic theorem of Mader asserts that every connected vertex‐transitive graph is maximally edge‐connected. We generalise this result to hypergraphs and show that every connected linear uniform vertex‐transitive hypergraph is maximally edge‐connected. We also show that if we relax either the linear or uniform conditions in this generalisation, then we can construct examples of vertex‐transitive hypergraphs which are not maximally edge‐connected.

Funder

Natural Sciences and Engineering Research Council of Canada

Publisher

Wiley

Subject

Geometry and Topology,Discrete Mathematics and Combinatorics

Reference10 articles.

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