{
  "id": "2206.11052",
  "version": "v1",
  "published": "2022-06-22T13:21:20.000Z",
  "updated": "2022-06-22T13:21:20.000Z",
  "title": "Bounds for the chromatic index of signed multigraphs",
  "authors": [
    "Eckhard Steffen",
    "Isaak H. Wolf"
  ],
  "comment": "7 pages; submitted for publication",
  "categories": [
    "math.CO"
  ],
  "abstract": "The paper studies edge-coloring of signed multigraphs and extends classical Theorems of Shannon and K\\\"onig to signed multigraphs. We prove that the chromatic index of a signed multigraph $(G,\\sigma_G)$ is at most $\\lfloor \\frac{3}{2} \\Delta(G) \\rfloor$. Furthermore, the chromatic index of a balanced signed multigraph $(H,\\sigma_H)$ is at most $\\Delta(H) + 1$ and the balanced signed multigraphs with chromatic index $\\Delta(H)$ are characterized.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-22T13:21:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "chromatic index",
      "balanced signed multigraph",
      "extends classical theorems",
      "paper studies edge-coloring"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}