{
  "id": "2305.18252",
  "version": "v1",
  "published": "2023-05-29T17:20:13.000Z",
  "updated": "2023-05-29T17:20:13.000Z",
  "title": "On MaxCut and the Lovász theta function",
  "authors": [
    "Igor Balla",
    "Oliver Janzer",
    "Benny Sudakov"
  ],
  "comment": "7 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this short note we prove a lower bound for the MaxCut of a graph in terms of the Lov\\'asz theta function of its complement. We combine this with known bounds on the Lov\\'asz theta function of complements of $H$-free graphs to recover many known results on the MaxCut of $H$-free graphs. In particular, we give a new, very short proof of a conjecture of Alon, Krivelevich and Sudakov about the MaxCut of graphs with no cycles of length $r$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-29T17:20:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lovász theta function",
      "lovasz theta function",
      "free graphs",
      "lower bound",
      "short note"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}