{
  "id": "1006.5280",
  "version": "v1",
  "published": "2010-06-28T07:58:50.000Z",
  "updated": "2010-06-28T07:58:50.000Z",
  "title": "Slim Sets of Binary Trees",
  "authors": [
    "Stefan Grünewald"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "A classical problem in phylogenetic tree analysis is to decide whether there is a phylogenetic tree $T$ that contains all information of a given collection $\\cP$ of phylogenetic trees. If the answer is \"yes\" we say that $\\cP$ is compatible and $T$ displays $\\cP$. This decision problem is NP-complete even if all input trees are quartets, that is binary trees with exactly four leaves. In this paper, we prove a sufficient condition for a set of binary phylogenetic trees to be compatible. That result is used to give a short and self-contained proof of the known characterization of quartet sets of minimal cardinality which are displayed by a unique phylogenetic tree.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-06-28T07:58:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "binary trees",
      "slim sets",
      "phylogenetic tree analysis",
      "binary phylogenetic trees",
      "unique phylogenetic tree"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1006.5280G"
    }
  }
}