{
  "id": "2501.02400",
  "version": "v1",
  "published": "2025-01-04T22:51:14.000Z",
  "updated": "2025-01-04T22:51:14.000Z",
  "title": "Skewness, crossing number and Euler's bound for graphs on surfaces",
  "authors": [
    "Paul C. Kainen"
  ],
  "comment": "16 pages, 57 references",
  "categories": [
    "math.CO"
  ],
  "abstract": "For every connected graph $G$ and surface $S$, we consider the well-known string of inequalities $\\delta_S(G) \\leq \\mu_S(G) \\leq \\nu_S(G)$, where $\\mu$ and $\\nu$ denote skewness and crossing number and $\\delta$ is the Euler-formula lower bound. Recent developments are surveyed; new results are given for the ``folded'' cube including its genus.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-01-04T22:51:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C10",
      "05C62",
      "57K20"
    ],
    "keywords": [
      "crossing number",
      "eulers bound",
      "euler-formula lower bound",
      "denote skewness",
      "connected graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}