{
  "id": "2309.15201",
  "version": "v1",
  "published": "2023-09-26T18:59:27.000Z",
  "updated": "2023-09-26T18:59:27.000Z",
  "title": "Mutual-visibility sets in Cartesian products of paths and cycles",
  "authors": [
    "Danilo Korže",
    "Aleksander Vesel"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "For a given graph $G$, the mutual-visibility problem asks for the largest set of vertices $M \\subseteq V(G)$ with the property that for any pair of vertices $u,v \\in M$ there exists a shortest $u,v$-path of $G$ that does not pass through any other vertex in $M$. The mutual-visibility problem for Cartesian products of a cycle and a path, as well as for Cartesian products of two cycles, is considered. Optimal solutions are provided for the majority of Cartesian products of a cycle and a path, while for the other family of graphs, the problem is completely solved.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-26T18:59:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cartesian products",
      "mutual-visibility sets",
      "mutual-visibility problem asks",
      "largest set",
      "optimal solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}