{
  "id": "1004.1430",
  "version": "v1",
  "published": "2010-04-08T21:50:38.000Z",
  "updated": "2010-04-08T21:50:38.000Z",
  "title": "Improved Bounds for $r$-Identifying Codes of the Hex Grid",
  "authors": [
    "Brendon Stanton"
  ],
  "comment": "12pp",
  "doi": "10.1137/100791610",
  "categories": [
    "math.CO"
  ],
  "abstract": "For any positive integer $r$, 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 pairwise distinct. For 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 find a code of density less than $5/(6r)$, which is sparser than the prior best construction which has density approximately $8/(9r)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-04-08T21:50:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "identifying code",
      "hex grid",
      "prior best construction",
      "infinite graphs",
      "positive integer"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1004.1430S"
    }
  }
}