{
  "id": "2405.09027",
  "version": "v1",
  "published": "2024-05-15T01:48:08.000Z",
  "updated": "2024-05-15T01:48:08.000Z",
  "title": "Csikvári's poset and Tutte polynomial",
  "authors": [
    "Changxin Ding"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Csikv\\'{a}ri constructed a poset on trees to prove that several graph functions attain extreme values at the star and the path among the trees on a fixed number of vertices. Reiner and Smith proved that the Tutte polynomials $T(1,y)$ of cones over trees, which are the graphs obtained by attaching a cone vertex to a tree, have the described extreme behavior. They further conjectured that the result can be strengthened in terms of Csikv\\'{a}ri's poset. We solve this conjecture affirmatively.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-15T01:48:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "tutte polynomial",
      "csikváris poset",
      "graph functions attain extreme values",
      "cone vertex"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}