{
  "id": "math/0606450",
  "version": "v1",
  "published": "2006-06-19T12:57:11.000Z",
  "updated": "2006-06-19T12:57:11.000Z",
  "title": "Drawings of Planar Graphs with Few Slopes and Segments",
  "authors": [
    "Vida Dujmovic'",
    "David Eppstein",
    "Matthew Suderman",
    "David R. Wood"
  ],
  "comment": "This paper is submitted to a journal. A preliminary version appeared as \"Really Straight Graph Drawings\" in the Graph Drawing 2004 conference. See http://arxiv.org/math/0606446 for a companion paper",
  "journal": "Computational Geometry: Theory and Applications 38:194-212, 2007",
  "doi": "10.1016/j.comgeo.2006.09.002",
  "categories": [
    "math.CO"
  ],
  "abstract": "We study straight-line drawings of planar graphs with few segments and few slopes. Optimal results are obtained for all trees. Tight bounds are obtained for outerplanar graphs, 2-trees, and planar 3-trees. We prove that every 3-connected plane graph on $n$ vertices has a plane drawing with at most ${5/2}n$ segments and at most $2n$ slopes. We prove that every cubic 3-connected plane graph has a plane drawing with three slopes (and three bends on the outerface). In a companion paper, drawings of non-planar graphs with few slopes are also considered.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-06-19T12:57:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "plane graph",
      "study straight-line drawings",
      "plane drawing",
      "optimal results",
      "non-planar graphs"
    ],
    "tags": [
      "conference paper",
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......6450D"
    }
  }
}