{
  "id": "math/0509397",
  "version": "v4",
  "published": "2005-09-18T09:30:19.000Z",
  "updated": "2007-12-03T15:50:19.000Z",
  "title": "Menger's theorem for infinite graphs",
  "authors": [
    "Ron Aharoni",
    "Eli Berger"
  ],
  "comment": "53 pages, final version submitted",
  "categories": [
    "math.CO"
  ],
  "abstract": "We prove that Menger's theorem is valid for infinite graphs, in the following strong form: let $A$ and $B$ be two sets of vertices in a possibly infinite digraph. Then there exist a set $\\cp$ of disjoint $A$-$B$ paths, and a set $S$ of vertices separating $A$ from $B$, such that $S$ consists of a choice of precisely one vertex from each path in $\\cp$. This settles an old conjecture of Erd\\H{o}s.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2007-12-03T15:50:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05"
    ],
    "keywords": [
      "infinite graphs",
      "mengers theorem",
      "strong form",
      "possibly infinite digraph",
      "old conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 53,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}