{
  "id": "2102.07894",
  "version": "v1",
  "published": "2021-02-15T23:34:54.000Z",
  "updated": "2021-02-15T23:34:54.000Z",
  "title": "The path-missing and path-free complexes of a directed graph",
  "authors": [
    "Darij Grinberg",
    "Lukas Katthän",
    "Joel Brewster Lewis"
  ],
  "comment": "33 pages",
  "categories": [
    "math.CO",
    "math.AT"
  ],
  "abstract": "We study the homotopy type and other properties of two simplicial complexes arising from a directed graph $G = (V, E)$ with two chosen vertices $s$ and $t$: the *path-free complex*, consisting of all subsets $F \\subseteq E$ that contain no path from $s$ to $t$, and the *path-missing complex*, its Alexander dual.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-15T23:34:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E45",
      "05C21",
      "05C31",
      "05A19"
    ],
    "keywords": [
      "directed graph",
      "path-free complexes",
      "path-missing",
      "homotopy type",
      "chosen vertices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}