{
  "id": "1902.00986",
  "version": "v1",
  "published": "2019-02-03T22:58:26.000Z",
  "updated": "2019-02-03T22:58:26.000Z",
  "title": "Decomposing split graphs into locally irregular graphs",
  "authors": [
    "Carla Negri Lintzmayer",
    "Guilherme Oliveira Mota",
    "Maycon Sambinelli"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "A graph is locally irregular if any pair of adjacent vertices have distinct degrees. A locally irregular decomposition of a graph $G$ is a decomposition $\\mathcal{D}$ of $G$ such that every subgraph $H \\in \\mathcal{D}$ is locally irregular. A graph is said to be decomposable if it admits a locally irregular decomposition. We prove that any decomposable split graph can be decomposed into at most three locally irregular subgraphs and we characterize all split graphs whose decomposition can be into one, two or three locally irregular subgraphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-03T22:58:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B40",
      "05C70"
    ],
    "keywords": [
      "locally irregular graphs",
      "decomposing split graphs",
      "locally irregular subgraphs",
      "locally irregular decomposition",
      "adjacent vertices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}