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arXiv · 2207.07536

The Edge-Connectivity of Vertex-Transitive Hypergraphs

Andrea C. Burgess·Robert D. Luther·David A. Pike
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Abstract

A 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.

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Andrea C. Burgess, Robert D. Luther, David A. Pike. 2023-09-29. The Edge-Connectivity of Vertex-Transitive Hypergraphs. https://arxiv.org/abs/2207.07536

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