{
  "id": "1501.03591",
  "version": "v1",
  "published": "2015-01-15T06:59:29.000Z",
  "updated": "2015-01-15T06:59:29.000Z",
  "title": "On the competition graphs of $d$-partial orders",
  "authors": [
    "Jihoon Choi",
    "Kyeong Seok Kim",
    "Suh-Ryung Kim",
    "Jung Yeun Lee",
    "Yoshio Sano"
  ],
  "comment": "14 pages, 5 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper, we study the competition graphs of $d$-partial orders and obtain their characterization which extends results given by Cho and Kim~\\cite{chokim} in 2005. We also show that any graph can be made into the competition graph of a $d$-partial order for some positive integer $d$ as long as adding isolated vertices is allowed. We then introduce the notion of the partial order competition dimension of a graph and study graphs whose partial order competition dimensions are at most three.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-15T06:59:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C20",
      "05C75"
    ],
    "keywords": [
      "competition graph",
      "partial order competition dimension",
      "study graphs",
      "extends results",
      "adding isolated vertices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}