{
  "id": "1401.7929",
  "version": "v3",
  "published": "2014-01-30T17:28:59.000Z",
  "updated": "2015-02-16T15:54:53.000Z",
  "title": "On Path-Pairability of Cartesian Product of Complete Bipartite Graphs",
  "authors": [
    "Gabor Meszaros"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We study inheritance of path-pairability in the Cartesian product of graphs, and prove di?erent (such as additive and multiplicative) inheritance patterns of path-pairability, depending on the size of the Cartesian product. We present path-pairable graph families, that improve the known upper bound on the minimal maximum degree of a path-pairable graph. Further results and open questions about path-pairability are also presented.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-03-17T17:05:41.000Z",
      "abstract": "We study path-pairability of Cartesian product of graphs and prove that the Cartesian product of the complete bipartite graph $K_{m,m}$ with itself is path-pairable. The result improves the known bound on the minimal value of the maximum degree of a path-pairable graph. Further results about path-pairability of graph products are presented.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-02-16T15:54:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complete bipartite graph",
      "cartesian product",
      "minimal value",
      "study path-pairability",
      "maximum degree"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.7929M"
    }
  }
}