{
  "id": "2010.02792",
  "version": "v1",
  "published": "2020-10-06T15:01:31.000Z",
  "updated": "2020-10-06T15:01:31.000Z",
  "title": "Optimal orientations of vertex-multiplications of cartesian products of graphs",
  "authors": [
    "W. H. W. Wong",
    "E. G. Tay"
  ],
  "comment": "29 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Koh and Tay proved a fundamental classification of $G$ vertex-multiplications into three classes $\\mathscr{C}_0, \\mathscr{C}_1$ and $\\mathscr{C}_2$. In this paper, we prove that vertex-multiplications of cartesian products of graphs $G\\times H$ lie in $\\mathscr{C}_0$ ($\\mathscr{C}_0\\cup \\mathscr{C}_1$ resp.) if $G^{(2)}\\in \\mathscr{C}_0$ ($\\mathscr{C}_1$ resp.), $d(G)\\ge 2$ and $d(G\\times H)\\ge 4$. We also focus on cartesian products involving trees, paths and cycles and show that most of them lie in $\\mathscr{C}_0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-06T15:01:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C12",
      "05C20",
      "05D05",
      "G.2.2",
      "F.2.2"
    ],
    "keywords": [
      "cartesian products",
      "optimal orientations",
      "vertex-multiplications",
      "fundamental classification"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}