{
  "id": "0901.1481",
  "version": "v2",
  "published": "2009-01-12T00:05:10.000Z",
  "updated": "2009-05-20T03:27:57.000Z",
  "title": "The tau constant and the edge connectivity of a metrized graph",
  "authors": [
    "Zubeyir Cinkir"
  ],
  "comment": "Various typos are corrected. Some minor changes made to the content. However, all the results remain the same. 27 pages, 6 figues",
  "categories": [
    "math.CO",
    "math.CA"
  ],
  "abstract": "The tau constant is an important invariant of a metrized graph, and it has applications in arithmetic properties of curves. We show how the tau constant of a metrized graph changes under successive edge contractions and deletions. We discover identities which we call \"contraction\", \"deletion\", and \"contraction-deletion\" identities on a metrized graph. By establishing a lower bound for the tau constant in terms of the edge connectivity, we prove that Baker and Rumely's lower bound conjecture on the tau constant holds for metrized graphs with edge connectivity 5 or more. We show that proving this conjecture for 3-regular graphs is enough to prove it for all graphs.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-05-20T03:27:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "edge connectivity",
      "rumelys lower bound conjecture",
      "tau constant holds",
      "arithmetic properties",
      "important invariant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0901.1481C"
    }
  }
}