{
  "id": "0903.2201",
  "version": "v1",
  "published": "2009-03-12T15:53:59.000Z",
  "updated": "2009-03-12T15:53:59.000Z",
  "title": "Flips in Graphs",
  "authors": [
    "Tom Bohman",
    "Andrzej Dudek",
    "Alan Frieze",
    "Oleg Pikhurko"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We study a problem motivated by a question related to quantum-error-correcting codes. Combinatorially, it involves the following graph parameter: $$f(G)=\\min\\set{|A|+|\\{x\\in V\\setminus A : d_A(x)\\text{is odd}\\}| : A\\neq\\emptyset},$$ where $V$ is the vertex set of $G$ and $d_A(x)$ is the number of neighbors of $x$ in $A$. We give asymptotically tight estimates of $f$ for the random graph $G_{n,p}$ when $p$ is constant. Also, if $$f(n)=\\max\\set{f(G): |V(G)|=n}$$ then we show that $f(n)\\leq (0.382+o(1))n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-03-12T15:53:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "graph parameter",
      "vertex set",
      "asymptotically tight estimates",
      "random graph",
      "quantum-error-correcting codes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.2201B"
    }
  }
}