{
  "id": "math/0609755",
  "version": "v1",
  "published": "2006-09-27T13:15:38.000Z",
  "updated": "2006-09-27T13:15:38.000Z",
  "title": "On (n, k)-extendable graphs and induced subgraphs",
  "authors": [
    "Guizhen Liu",
    "Qinglin Yu"
  ],
  "comment": "8 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $G$ be a graph with vertex set $V(G)$. Let $n$ and $k$ be non-negative integers such that $n + 2k \\leq |V(G)| - 2$ and $|V(G)| - n$ is even. If when deleting any $n$ vertices of $G$ the remaining subgraph contains a matching of $k$ edges and every $k$-matching can be extended to a 1-factor, then $G$ is called an $(n, k)-extendable graph. In this paper we present several results about $(n, k)$-extendable graphs and its subgraphs. In particular, we proved that if $G - V(e)$ is $(n, k)$-extendable graph for each $e \\in F$ (where $F$ is a fixed 1-factor in $G$), then $G$ is $(n, k)$-extendable graph.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-09-27T13:15:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C70"
    ],
    "keywords": [
      "induced subgraphs",
      "vertex set",
      "remaining subgraph contains"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......9755L"
    }
  }
}