{
  "id": "1104.5261",
  "version": "v1",
  "published": "2011-04-27T22:11:33.000Z",
  "updated": "2011-04-27T22:11:33.000Z",
  "title": "Isomorph-free generation of 2-connected graphs with applications",
  "authors": [
    "Derrick Stolee"
  ],
  "comment": "15 pages, 3 figures, 4 tables",
  "categories": [
    "math.CO"
  ],
  "abstract": "Many interesting graph families contain only 2-connected graphs, which have ear decompositions. We develop a technique to generate families of unlabeled 2-connected graphs using ear augmentations and apply this technique to two problems. In the first application, we search for uniquely K_r-saturated graphs and find the list of uniquely K_4-saturated graphs on at most 12 vertices, supporting current conjectures for this problem. In the second application, we verifying the Edge Reconstruction Conjecture for all 2-connected graphs on at most 12 vertices. This technique can be easily extended to more problems concerning 2-connected graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-04-27T22:11:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C85"
    ],
    "keywords": [
      "isomorph-free generation",
      "interesting graph families contain",
      "edge reconstruction conjecture",
      "ear decompositions",
      "second application"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1104.5261S"
    }
  }
}