{
  "id": "2308.09491",
  "version": "v1",
  "published": "2023-08-18T12:00:36.000Z",
  "updated": "2023-08-18T12:00:36.000Z",
  "title": "A note on removable edges in near-bricks",
  "authors": [
    "Deyu Wu",
    "Yipei Zhang",
    "Xiumei Wang"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "An edge $e$ of a matching covered graph $G$ is removable if $G-e$ is also matching covered. Carvalho, Lucchesi, and Murty showed that every brick $G$ different from $K_4$ and $\\overline{C_6}$ has at least $\\Delta-2$ removable edges, where $\\Delta$ is the maximum degree of $G$. In this paper, we generalize the result to irreducible near-bricks, where a graph is irreducible if it contains no induced odd path of length three or more.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-18T12:00:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "removable edges",
      "maximum degree",
      "induced odd path",
      "matching covered graph",
      "irreducible near-bricks"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}