{
  "id": "2305.08442",
  "version": "v1",
  "published": "2023-05-15T08:40:16.000Z",
  "updated": "2023-05-15T08:40:16.000Z",
  "title": "Crowns in pseudo-random graphs and Hamilton cycles in their squares",
  "authors": [
    "Michael Krivelevich"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "A crown with $k$ spikes is an edge-disjoint union of a cycle $C$ and a matching $M$ of size $k$ such that each edge of $M$ has exactly one vertex in common with $C$. We prove that if $G$ is an $(n,d,\\lambda)$-graph with $\\lambda/d\\le 0.001$ and $d$ is large enough, then $G$ contains a crown on $n$ vertices with $\\lfloor n/2\\rfloor$ spikes. As a consequence, such $G$ contains a Hamilton cycle in its square $G^2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-15T08:40:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C80",
      "05C45"
    ],
    "keywords": [
      "hamilton cycle",
      "pseudo-random graphs",
      "edge-disjoint union",
      "consequence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}