{
  "id": "2204.07132",
  "version": "v1",
  "published": "2022-04-14T17:42:04.000Z",
  "updated": "2022-04-14T17:42:04.000Z",
  "title": "On Merino--Welsh conjecture for split matroids",
  "authors": [
    "Luis Ferroni",
    "Benjamin Schröter"
  ],
  "comment": "5 pages, 1 figure",
  "categories": [
    "math.CO"
  ],
  "abstract": "In 1999 Merino and Welsh conjectured that evaluations of the Tutte polynomial of a graph satisfy an inequality. In this short article we show that the conjecture generalized to matroids holds for the large class of all split matroids by exploiting the structure of their lattice of cyclic flats. This class of matroids strictly contains all paving and copaving matroids.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-14T17:42:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B35",
      "05C31"
    ],
    "keywords": [
      "split matroids",
      "merino-welsh conjecture",
      "graph satisfy",
      "tutte polynomial",
      "short article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}