{
  "id": "1711.08116",
  "version": "v1",
  "published": "2017-11-22T02:52:11.000Z",
  "updated": "2017-11-22T02:52:11.000Z",
  "title": "Arc index of spatial graphs",
  "authors": [
    "Minjung Lee",
    "Sungjong No",
    "Seungsang Oh"
  ],
  "categories": [
    "math.GT"
  ],
  "abstract": "Bae and Park found an upper bound on the arc index of prime links in terms of the minimal crossing number. In this paper, we extend the definition of the arc presentation to spatial graphs and find an upper bound on the arc index $\\alpha (G)$ of any spatial graph $G$ as $$\\alpha(G) \\leq c(G)+e+b,$$ where $c(G)$ is the minimal crossing number of $G$, $e$ is the number of edges, and $b$ is the number of bouquet cut-components. This upper bound is lowest possible.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-22T02:52:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27"
    ],
    "keywords": [
      "spatial graph",
      "arc index",
      "upper bound",
      "minimal crossing number",
      "prime links"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}