{
  "id": "1501.05619",
  "version": "v1",
  "published": "2015-01-22T20:09:27.000Z",
  "updated": "2015-01-22T20:09:27.000Z",
  "title": "Local colourings and monochromatic partitions in complete bipartite graphs",
  "authors": [
    "Richard Lang",
    "Maya Stein"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We show that for any $2$-local colouring of the edges of a complete bipartite graph, its vertices can be covered with at most $3$ disjoint monochromatic paths. And, we can cover almost all vertices of any complete or complete bipartite $r$-locally coloured graph with $O(r^2)$ disjoint monochromatic cycles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-22T20:09:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C38",
      "05C55"
    ],
    "keywords": [
      "complete bipartite graph",
      "monochromatic partitions",
      "local colouring",
      "disjoint monochromatic paths",
      "disjoint monochromatic cycles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}