{
  "id": "1204.1444",
  "version": "v2",
  "published": "2012-04-06T09:55:33.000Z",
  "updated": "2014-06-13T09:34:41.000Z",
  "title": "Computing the minimum rank of a loop directed tree",
  "authors": [
    "Maguy Trefois",
    "Jean-Charles Delvenne"
  ],
  "comment": "This paper has been withdrawn due to a crucial error in Lemma 5.2. A correct and more complete version is available here: arXiv:1405.6222. In particular, in this new version we identify a class of directed trees allowing loops whose minimum rank is computable in linear time. An efficient algorithm for the minimum rank of any directed tree allowing loops is still needed",
  "categories": [
    "math.CO"
  ],
  "abstract": "The minimum rank of a graph is the minimum possible rank of a real matrix whose zero-nonzero pattern is described by the graph. The current algorithms can compute efficiently the minimum rank of undirected trees. This paper provides an algorithm to compute in polynomial time the minimum rank of directed trees allowing loops.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-06-13T09:34:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "minimum rank",
      "loop directed tree",
      "real matrix",
      "current algorithms",
      "polynomial time"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.1444T"
    }
  }
}