{
  "id": "2302.04050",
  "version": "v1",
  "published": "2023-02-08T13:44:14.000Z",
  "updated": "2023-02-08T13:44:14.000Z",
  "title": "Optimal bisections of directed graphs",
  "authors": [
    "Guanwu Liu",
    "Jie Ma",
    "Chunlei Zu"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper, motivated by a problem of Scott and a conjecture of Lee, Loh and Sudakov we consider bisections of directed graphs. We prove that every directed graph with $m$ arcs and minimum semidegree at least $d$ admits a bisection in which at least $\\left(\\frac{d}{2(2d+1)}+o(1)\\right)m$ arcs cross in each direction. This provides an optimal bound as well as a positive answer to a question of Hou and Wu in a stronger form.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-02-08T13:44:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "directed graph",
      "optimal bisections",
      "minimum semidegree",
      "arcs cross",
      "optimal bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}