{
  "id": "1802.01114",
  "version": "v1",
  "published": "2018-02-04T12:29:36.000Z",
  "updated": "2018-02-04T12:29:36.000Z",
  "title": "Multicoloring of Graphs to Secure a Secret",
  "authors": [
    "Tanja Vojković",
    "Damir Vukičević",
    "Vinko Zlatić"
  ],
  "comment": "19 pages, 5 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "Vertex coloring and multicoloring of graphs are a well known subject in graph theory, as well as their applications. In vertex multicoloring, each vertex is assigned some subset of a given set of colors. Here we propose a new kind of vertex multicoloring, motivated by the situation of sharing a secret and securing it from the actions of some number of attackers. We name the multicoloring a highly $a$-resistant vertex $k$-multicoloring, where $a$ is the number of the attackers, and $k$ the number of colors. For small values $a$ we determine what is the minimal number of vertices a graph must have in order to allow such a coloring, and what is the minimal number of colors needed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-04T12:29:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15"
    ],
    "keywords": [
      "minimal number",
      "vertex multicoloring",
      "graph theory",
      "resistant vertex",
      "small values"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}