{
  "id": "1004.3281",
  "version": "v1",
  "published": "2010-04-19T19:13:32.000Z",
  "updated": "2010-04-19T19:13:32.000Z",
  "title": "Lower bounds for identifying codes in some infinite grids",
  "authors": [
    "Ryan Martin",
    "Brendon Stanton"
  ],
  "comment": "18pp",
  "categories": [
    "math.CO"
  ],
  "abstract": "An $r$-identifying code on a graph $G$ is a set $C\\subset V(G)$ such that for every vertex in $V(G)$, the intersection of the radius-$r$ closed neighborhood with $C$ is nonempty and unique. On a finite graph, the density of a code is $|C|/|V(G)|$, which naturally extends to a definition of density in certain infinite graphs which are locally finite. We present new lower bounds for densities of codes for some small values of $r$ in both the square and hexagonal grids.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-04-19T19:13:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lower bounds",
      "identifying code",
      "infinite grids",
      "infinite graphs",
      "hexagonal grids"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1004.3281M"
    }
  }
}