{
  "id": "1903.09725",
  "version": "v1",
  "published": "2019-03-22T22:27:38.000Z",
  "updated": "2019-03-22T22:27:38.000Z",
  "title": "Large homogeneous subgraphs in bipartite graphs with forbidden induced subgraphs",
  "authors": [
    "Maria Axenovich",
    "Casey Tompkins",
    "Lea Weber"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "For a bipartite graph G, let h(G) be the largest t such that either G or the bipartite complement of G contain K_{t,t}. For a class F of graphs, let h(F)= min {h(G): G\\in F}. We say that a bipartite graph H is strongly acyclic if neither H nor its bipartite complement contain a cycle. By Forb(n, H) we denote a set of bipartite graphs with parts of sizes n each, that do not contain H as an induced bipartite subgraph respecting the sides. One can easily show that h(Forb(n,H))= O(n^{1-s}) for a positive s if H is not strongly acyclic. Here, we prove that h(Forb(n, H)) is linear in n for all strongly acyclic graphs except for four graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-22T22:27:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bipartite graph",
      "forbidden induced subgraphs",
      "large homogeneous subgraphs",
      "bipartite complement contain",
      "induced bipartite subgraph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}