{
  "id": "1702.03060",
  "version": "v1",
  "published": "2017-02-10T03:53:20.000Z",
  "updated": "2017-02-10T03:53:20.000Z",
  "title": "A Variation of the Erdős-Sós Conjecture in Bipartite Graphs",
  "authors": [
    "Long-Tu Yuan",
    "Xiao-Dong Zhang"
  ],
  "comment": "22 pages 2figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "The Erd\\H{o}s-S\\'{o}s Conjecture states that every graph with average degree more than $k-2$ contains all trees of order $k$ as subgraphs. In this paper, we consider a variation of the above conjecture: studying the maximum size of an $(n,m)$-bipartite graph which does not contain all $(k,l)$-bipartite trees for given integers $n\\ge m$ and $k\\ge l$. In particular, we determine that the maximum size of an $(n,m)$-bipartite graph which does not contain all $(n,m)$-bipartite trees as subgraphs (or all $(k,2)$-bipartite trees as subgraphs, respectively). Furthermore, all these extremal graphs are characterized.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-10T03:53:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C35",
      "05C05"
    ],
    "keywords": [
      "bipartite graph",
      "erdős-sós conjecture",
      "bipartite trees",
      "extremal graphs",
      "average degree"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}