{
  "id": "1608.07255",
  "version": "v1",
  "published": "2016-08-25T19:01:14.000Z",
  "updated": "2016-08-25T19:01:14.000Z",
  "title": "Combinatorial characterization of upward planarity",
  "authors": [
    "Xuexing Lu",
    "Yu Ye"
  ],
  "comment": "12 pages, 5 figures",
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "For any acyclic directed graph $G$, we introduce two notions: one is called an upward planar order on $G$ which is a linear extension of the edge poset of $G$ with some constraints, the other is called a canonical progressive planar extension (CPP extension for short) of $G$ which is an embedding of $G$ into a progressive planar graph with some constraints. Based on new characterizations of progressive planar graphs, we show that there is a natural bijection between the set of upward planar orders of $G$ and the set of CPP extensions of $G$. Finally we justify the combinatorial definition that an upward planar graph is an acyclic directed graph with an upward planar order.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-25T19:01:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "upward planar order",
      "combinatorial characterization",
      "upward planarity",
      "acyclic directed graph",
      "progressive planar graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}