{
  "abstract": "An $(r,z,g)$-mixed cage is a mixed graph that is $r$-regular in edges, $z$-regular in arcs, of girth $g$ and of minimum order $n=n(r,z,g)$. We give a general lower bound for $n(r,z,g)$. In the case $g=3$, we determine the exact value $n(r,z,3)=r+2z+1$. For $g=4$ we give two improved lower bounds and we determine the exact value $n(r,z,4)=2r+4z$ for $r\\geq 2z-2$. We also present computational results, obtaining mixed cages and computational lower bounds by means of exhaustive backtracking searches with symmetry reductions. Moreover, we give an upper bound for $n(1,z,g)$ that matches all our computed values.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14110",
  "author_total": 2,
  "authors": [
    {
      "name": "Claudia Marlene De la Cruz"
    },
    {
      "name": "Miguel Ángel Pizaña"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/enyjkqgx3ymfy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14110",
  "fulltext_url": null,
  "id": "enyjkqgx3ymfy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.14110",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7221792206",
  "pdf_url": "https://arxiv.org/pdf/2610.14110",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/enyjkqgx3ymfy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.14110",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14110"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "New mixed cages, bounds and computational results",
  "title_text": "New mixed cages, bounds and computational results",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/enyjkqgx3ymfy",
  "venue": "arXiv",
  "versions": []
}