{
  "id": "1110.2945",
  "version": "v2",
  "published": "2011-10-13T13:56:40.000Z",
  "updated": "2013-10-10T21:58:03.000Z",
  "title": "Highly arc-transitive digraphs -- counterexamples and structure",
  "authors": [
    "Matt DeVos",
    "Bojan Mohar",
    "Robert Šámal"
  ],
  "comment": "18 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We resolve two problems of [Cameron, Praeger, and Wormald -- Infinite highly arc transitive digraphs and universal covering digraphs, Combinatorica 1993]. First, we construct a locally finite highly arc-transitive digraph with universal reachability relation. Second, we provide constructions of 2-ended highly arc transitive digraphs where each `building block' is a finite bipartite graph that is not a disjoint union of complete bipartite graphs. This was conjectured impossible in the above paper. We also describe the structure of 2-ended highly arc transitive digraphs in more generality, although complete characterization remains elusive.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-10-10T21:58:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E18",
      "05C63"
    ],
    "keywords": [
      "counterexamples",
      "universal reachability relation",
      "finite bipartite graph",
      "infinite highly arc transitive digraphs",
      "complete bipartite graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.2945D"
    }
  }
}