{
  "id": "2301.09493",
  "version": "v1",
  "published": "2023-01-23T15:42:47.000Z",
  "updated": "2023-01-23T15:42:47.000Z",
  "title": "Functionality of box intersection graphs",
  "authors": [
    "Clément Dallard",
    "Vadim Lozin",
    "Martin Milanič",
    "Kenny Štorgel",
    "Viktor Zamaraev"
  ],
  "comment": "11 pages",
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "Functionality is a graph complexity measure that extends a variety of parameters, such as vertex degree, degeneracy, clique-width, or twin-width. In the present paper, we show that functionality is bounded for box intersection graphs in $\\mathbb{R}^1$, i.e. for interval graphs, and unbounded for box intersection graphs in $\\mathbb{R}^3$. We also study a parameter known as symmetric difference, which is intermediate between twin-width and functionality, and show that this parameter is unbounded both for interval graphs and for unit box intersection graphs in $\\mathbb{R}^2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-23T15:42:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C75",
      "05C62"
    ],
    "keywords": [
      "functionality",
      "interval graphs",
      "unit box intersection graphs",
      "graph complexity measure",
      "vertex degree"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}