{
  "id": "2106.12099",
  "version": "v1",
  "published": "2021-06-22T23:29:40.000Z",
  "updated": "2021-06-22T23:29:40.000Z",
  "title": "Structural properties of bipartite subgraphs",
  "authors": [
    "Robert Hickingbotham",
    "David R. Wood"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "This paper establishes sufficient conditions that force a graph to contain a bipartite subgraph with a given structural property. In particular, let $\\beta$ be any of the following graph parameters: Hadwiger number, Haj\\'{o}s number, treewidth, pathwidth, and treedepth. In each case, we show that there exists a function $f$ such that every graph $G$ with $\\beta(G)\\geq f(k)$ contains a bipartite subgraph $\\hat{G}\\subseteq G$ with $\\beta(\\hat{G})\\geq k$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-22T23:29:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bipartite subgraph",
      "structural property",
      "paper establishes sufficient conditions",
      "hadwiger number",
      "graph parameters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}