The Edge-Connectivity of Vertex-Transitive Hypergraphs
Combinatorics
2023-10-02 v3
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.
Cite
@article{arxiv.2207.07536,
title = {The Edge-Connectivity of Vertex-Transitive Hypergraphs},
author = {Andrea C. Burgess and Robert D. Luther and David A. Pike},
journal= {arXiv preprint arXiv:2207.07536},
year = {2023}
}
Comments
8 pages