{
  "abstract": "We prove Pisanski's conjecture on quadrilateral embeddings of regular bipartite graphs. For integers $m\\geq d\\geq4$ with $4\\mid md$, we construct both a connected simple $d$-regular bipartite graph $G$ with $m$ vertices in each bipartition class and an orientable quadrangulation. This graph's genus is \\[ \\ga(G)=1+\\frac{m(d-4)}4. \\] These quadrangulations attain the lower bound on the genus from Euler's formula. We give dihedral constructions for even $m$ and a cyclic construction for every $m\\geq d$ with $4\\mid d$. In each case, two cyclic permutations of a connection set of size $d$ determine all of the local rotations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13085",
  "author_total": 2,
  "authors": [
    {
      "name": "Austin Ulrigg"
    },
    {
      "name": "Alexander Metzger"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cy5zqtef2cbhc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13085",
  "fulltext_url": null,
  "id": "cy5zqtef2cbhc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13085",
  "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": "W7221577814",
  "pdf_url": "https://arxiv.org/pdf/2610.13085",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cy5zqtef2cbhc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.13085",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13085"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Resolving Pisanski's Conjecture",
  "title_text": "Resolving Pisanski's Conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/cy5zqtef2cbhc",
  "venue": "arXiv",
  "versions": []
}