{
  "id": "2012.10123",
  "version": "v1",
  "published": "2020-12-18T09:29:17.000Z",
  "updated": "2020-12-18T09:29:17.000Z",
  "title": "Hamiltonian properties in generalized lexicographic products",
  "authors": [
    "Jan Ekstein",
    "Jakub Teska"
  ],
  "comment": "18 pages, 2 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "The lexicographic product $G[H]$ of two graphs $G$ and $H$ is obtained from $G$ by replacing each vertex with a copy of $H$ and adding all edges between any pair of copies corresponding to adjacent vertices of $G$. We generalize the lexicographic product such that we replace each vertex of $G$ with arbitrary graph on the same number of vertices. We present sufficient and necessary conditions for traceability, hamiltonicity and hamiltonian connectivity of $G[H]$ if $G$ is a path.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-18T09:29:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C76",
      "05C45"
    ],
    "keywords": [
      "generalized lexicographic products",
      "hamiltonian properties",
      "adjacent vertices",
      "arbitrary graph",
      "necessary conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}