{
  "id": "1705.09957",
  "version": "v1",
  "published": "2017-05-28T16:16:37.000Z",
  "updated": "2017-05-28T16:16:37.000Z",
  "title": "Proof of a local antimagic conjecture",
  "authors": [
    "John Haslegrave"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "An antimagic labelling of a graph $G$ is a bijection $f:E(G)\\to\\{1,\\ldots,E(G)\\}$ such that the sums $S_v=\\sum_{e\\ni v}f(e)$ distinguish all vertices. A well-known conjecture of Hartsfield and Ringel is that every connected graph other than $K_2$ admits an antimagic labelling. Recently, two sets of authors (Arumugam, Premalatha, Ba\\v{c}a \\& Semani\\v{c}ov\\'a-Fe\\v{n}ov\\v{c}\\'ikov\\'a, and Bensmail, Senhaji \\& Lyngsie) independently introduced the weaker notion of a local antimagic labelling, where only adjacent vertices must be distinguished. Both sets of authors conjectured that any connected graph other than $K_2$ admits a local antimagic labelling. We prove this latter conjecture using the probabilistic method.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-28T16:16:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C78",
      "05C15"
    ],
    "keywords": [
      "local antimagic conjecture",
      "local antimagic labelling",
      "connected graph",
      "well-known conjecture",
      "weaker notion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}