{
  "id": "1710.05936",
  "version": "v1",
  "published": "2017-10-16T18:00:45.000Z",
  "updated": "2017-10-16T18:00:45.000Z",
  "title": "Embedding an Edge-colored $K(a^{(p)};λ,μ)$ into a Hamiltonian Decomposition of $K(a^{(p+r)};λ,μ)$",
  "authors": [
    "Amin Bahmanian",
    "Chris Rodger"
  ],
  "comment": "10 pages, 2 figures",
  "journal": "Graphs Combin. 29 (2013), no. 4, 747-755",
  "doi": "10.1007/s00373-012-1164-0",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $K(a^{(p)};\\lambda,\\mu )$ be a graph with $p$ parts, each part having size $a$, in which the multiplicity of each pair of vertices in the same part (in different parts) is $\\lambda$ ($\\mu $, respectively). In this paper we consider the following embedding problem: When can a graph decomposition of $K(a^{(p)};\\lambda,\\mu )$ be extended to a Hamiltonian decomposition of $K(a^{(p+r)};\\lambda,\\mu )$ for $r>0$? A general result is proved, which is then used to solve the embedding problem for all $r\\geq \\frac{\\lambda}{\\mu a}+\\frac{p-1}{a-1}$. The problem is also solved when $r$ is as small as possible in two different senses, namely when $r=1$ and when $r=\\frac{\\lambda}{\\mu a}-p+1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-16T18:00:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C70",
      "05C15",
      "05C38",
      "05C45",
      "05C51"
    ],
    "keywords": [
      "hamiltonian decomposition",
      "embedding problem",
      "graph decomposition",
      "general result"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}