{
  "id": "0711.2846",
  "version": "v1",
  "published": "2007-11-19T06:31:55.000Z",
  "updated": "2007-11-19T06:31:55.000Z",
  "title": "Rainbow number of matchings in regular bipartite graphs",
  "authors": [
    "Xueliang Li",
    "Zhixia Xu"
  ],
  "comment": "9 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Given a graph $G$ and a subgraph $H$ of $G$, let $rb(G,H)$ be the minimum number $r$ for which any edge-coloring of $G$ with $r$ colors has a rainbow subgraph $H$. The number $rb(G,H)$ is called the rainbow number of $H$ with respect to $G$. Denote $mK_2$ a matching of size $m$ and $B_{n,k}$ a $k$-regular bipartite graph with bipartition $(X,Y)$ such that $|X|=|Y|=n$ and $k\\leq n$. In this paper we give an upper and lower bound for $rb(B_{n,k},mK_2)$, and show that for given $k$ and $m$, if $n$ is large enough, $rb(B_{n,k},mK_2)$ can reach the lower bound. We also determine the rainbow number of matchings in paths and cycles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-11-19T06:31:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15",
      "05C35",
      "05C55",
      "05C70"
    ],
    "keywords": [
      "regular bipartite graph",
      "rainbow number",
      "lower bound",
      "rainbow subgraph",
      "minimum number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0711.2846L"
    }
  }
}