{
  "id": "1309.1835",
  "version": "v2",
  "published": "2013-09-07T08:15:32.000Z",
  "updated": "2013-09-22T19:25:03.000Z",
  "title": "Claw-freeness, 3-homogeneous subsets of a graph and a reconstruction problem",
  "authors": [
    "Maurice Pouzet",
    "Hamza Si Kaddour",
    "Nicolas Trotignon"
  ],
  "comment": "This paper has no DOI, published version available at: http://cdm.ucalgary.ca/cdm/index.php/cdm/article/view/189",
  "journal": "Contributions to Discrete Mathematics, 6(1):92-103, 2011",
  "categories": [
    "math.CO"
  ],
  "abstract": "We describe ${\\rm Forb}\\{K_{1,3}, \\bar {K_{1,3}}\\}$, the class of graphs $G$ such that $G$ and its complement $\\bar{G}$ are claw-free. With few exceptions, it is made of graphs whose connected components consist of cycles of length at least 4, paths, and of the complements of these graphs. Considering the hypergraph ${\\mathcal H}^{(3)}(G)$ made of the 3-element subsets of the vertex set of a graph $G$ on which $G$ induces a clique or an independent subset, we deduce from above a description of the Boolean sum $G\\dot{+}G'$ of two graphs $G$ and $G'$ giving the same hypergraph. We indicate the role of this latter description in a reconstruction problem of graphs up to complementation.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-09-22T19:25:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C60"
    ],
    "keywords": [
      "reconstruction problem",
      "claw-freeness",
      "connected components consist",
      "hypergraph",
      "vertex set"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.1835P"
    }
  }
}