{
  "id": "1207.3319",
  "version": "v1",
  "published": "2012-07-13T18:00:50.000Z",
  "updated": "2012-07-13T18:00:50.000Z",
  "title": "Lower bound for the rank of rigidity matrix of 4-valent graphs under various connectivity assumptions",
  "authors": [
    "Shisen Luo"
  ],
  "comment": "15 pages, 5 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper we study the rank of planar rigidity matrix of 4-valent graphs, both in case of generic realizations and configurations in general position, under various connectivity assumptions on the graphs. For each case considered, we prove a lower bound and provide an example which shows the order of the bound we proved is sharp. This work is closed related to work in \\cite{Luo:Rigidity} and answers some questions raised there.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-07-13T18:00:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52C25",
      "05C50"
    ],
    "keywords": [
      "lower bound",
      "connectivity assumptions",
      "planar rigidity matrix",
      "generic realizations",
      "general position"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.3319L"
    }
  }
}