{
  "id": "math/0508647",
  "version": "v1",
  "published": "2005-08-31T17:52:10.000Z",
  "updated": "2005-08-31T17:52:10.000Z",
  "title": "Hamiltonicity of Cubic Cayley Graphs",
  "authors": [
    "Henry Glover",
    "Dragan Marusic"
  ],
  "comment": "13 pages, 6 figures",
  "categories": [
    "math.CO",
    "math.GR"
  ],
  "abstract": "Following a problem posed by Lov\\'asz in 1969, it is believed that every connected vertex-transitive graph has a Hamilton path. This is shown here to be true for cubic Cayley graphs arising from groups having a $(2,s,3)$-presentation, that is, for groups $G=\\la a,b| a^2=1, b^s=1, (ab)^3=1, etc. \\ra$ generated by an involution $a$ and an element $b$ of order $s\\geq3$ such that their product $ab$ has order 3. More precisely, it is shown that the Cayley graph $X=Cay(G,\\{a,b,b^{-1}\\})$ has a Hamilton cycle when $|G|$ (and thus $s$) is congruent to 2 modulo 4, and has a long cycle missing only two vertices (and thus necessarily a Hamilton path) when $|G|$ is congruent to 0 modulo 4.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-08-31T17:52:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C25",
      "20B25"
    ],
    "keywords": [
      "hamilton path",
      "hamiltonicity",
      "cubic cayley graphs arising",
      "hamilton cycle",
      "long cycle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......8647G"
    }
  }
}