{
  "id": "1307.6443",
  "version": "v1",
  "published": "2013-07-24T14:58:00.000Z",
  "updated": "2013-07-24T14:58:00.000Z",
  "title": "Clique numbers of graph unions",
  "authors": [
    "Maria Chudnovsky",
    "Juba Ziani"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $B$ and $R$ be two simple graphs with vertex set $V$, and let $G(B,R)$ be the simple graph with vertex set $V$, in which two vertices are adjacent if they are adjacent in at least one of $B$ and $R$. For $X \\subseteq V$, we denote by $B|X$ the subgraph of $B$ induced by $X$; let $R|X$ and $G(B,R)|X$ be defined similarly. We say that the pair $(B,R)$ is {\\em additive} if for every $X \\subseteq V$, the sum of the clique numbers of $B|X$ and $R|X$ is at least the clique number of $G(B,R)|X$. In this paper we give a necessary and sufficient characterization of additive pairs of graphs. This is a numerical variant of a structural question studied in \\cite{ABC}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-07-24T14:58:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "clique number",
      "graph unions",
      "simple graph",
      "vertex set",
      "sufficient characterization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.6443C"
    }
  }
}