{
  "id": "2207.07536",
  "version": "v1",
  "published": "2022-07-15T15:28:05.000Z",
  "updated": "2022-07-15T15:28:05.000Z",
  "title": "The Edge-Connectivity of Vertex-Transitive Hypergraphs",
  "authors": [
    "Andrea C. Burgess",
    "Robert D. Luther",
    "David A. Pike"
  ],
  "comment": "8 pages",
  "categories": [
    "math.CO"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-15T15:28:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C40",
      "05E18",
      "05C65"
    ],
    "keywords": [
      "edge-connectivity",
      "connected linear uniform vertex-transitive hypergraph",
      "automorphism group acts",
      "mader asserts",
      "classic theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}