{
  "id": "1905.09101",
  "version": "v1",
  "published": "2019-05-22T12:30:54.000Z",
  "updated": "2019-05-22T12:30:54.000Z",
  "title": "Gaps in the cycle spectrum of 3-connected cubic planar graphs",
  "authors": [
    "Martin Merker"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We prove that, for every natural number $k$, every sufficiently large 3-connected cubic planar graph has a cycle whose length is in $[k,2k+9]$. We also show that this bound is close to being optimal by constructing, for every even $k\\geq 4$, an infinite family of 3-connected cubic planar graphs that contain no cycle whose length is in $[k,2k+1]$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-22T12:30:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cubic planar graph",
      "cycle spectrum",
      "natural number",
      "sufficiently large"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}