{
  "id": "1604.02088",
  "version": "v1",
  "published": "2016-04-07T17:50:03.000Z",
  "updated": "2016-04-07T17:50:03.000Z",
  "title": "Max k-cut and the smallest eigenvalue",
  "authors": [
    "V. Nikiforov"
  ],
  "comment": "5 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $G$ be a graph of order $n$ and size $m$, and let $\\mathrm{mc}_{k}\\left( G\\right) $ be the maximum size of a $k$-cut of $G.$ It is shown that \\[ \\mathrm{mc}_{k}\\left( G\\right) \\leq\\frac{k-1}{k}\\left( m-\\frac{\\mu_{\\min }\\left( G\\right) n}{2}\\right) , \\] where $\\mu_{\\min}\\left( G\\right) $ is the smallest eigenvalue of the adjacency matrix of $G.$ An infinite class of graphs forcing equality in this bound is constructed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-07T17:50:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50"
    ],
    "keywords": [
      "smallest eigenvalue",
      "max k-cut",
      "adjacency matrix",
      "infinite class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160402088N"
    }
  }
}