{
  "id": "1511.09301",
  "version": "v1",
  "published": "2015-11-30T13:32:29.000Z",
  "updated": "2015-11-30T13:32:29.000Z",
  "title": "$m$-Cycle Packings of $(λ+μ)K_{v+u}-λK_v$: $m$ even",
  "authors": [
    "John Asplund"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "A $\\lambda K_v$ is a complete graph on $v$ vertices with $\\lambda$ edges between each pair of the $v$ vertices. A $(\\lambda+\\mu)K_{v+u}-\\lambda K_v$ is a $(\\lambda+\\mu)K_{v+u}$ with the edge set of $\\lambda K_v$ removed. Decomposing a $(\\lambda+\\mu)K_{v+u}-\\lambda K_v$ into edge-disjoint $m$-cycles has been studied by many people within the last $10$ years. Past results have only managed to solve this problem for $m=4$ and partial results when $m=3$ or $m=5$. In this paper, we are able to solve this problem for all even cycle lengths as long as $u,v\\geq m+2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-30T13:32:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C51"
    ],
    "keywords": [
      "cycle packings",
      "complete graph",
      "edge set",
      "past results",
      "partial results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}