{
  "id": "1812.06715",
  "version": "v1",
  "published": "2018-12-17T11:41:43.000Z",
  "updated": "2018-12-17T11:41:43.000Z",
  "title": "Caterpillars are Antimagic",
  "authors": [
    "Antoni Lozano",
    "Mercè Mora",
    "Carlos Seara",
    "Joaquín Tey"
  ],
  "comment": "9 pages, 1 figure",
  "categories": [
    "math.CO"
  ],
  "abstract": "An antimagic labeling of a graph $G$ is an injection from $E(G)$ to $\\{1,2,\\dots,|E(G)|\\}$ such that all vertex sums are pairwise distinct, where the vertex sum at vertex $u$ is the sum of the labels assigned to edges incident to $u$. A graph is called antimagic when it has an antimagic labeling. Hartsfield and Ringel conjectured that every simple connected graph other than $K_2$ is antimagic and the conjecture remains open even for trees. Here we prove that caterpillars are antimagic by means of an $O(n \\log n)$ algorithm.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-17T11:41:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C78"
    ],
    "keywords": [
      "caterpillars",
      "vertex sum",
      "conjecture remains open",
      "simple connected graph",
      "antimagic labeling"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}