{
  "abstract": "We determine the orientable genus of an infinite family of bipartite Kneser graphs. The graph $H(h,2)$ has two copies of the two-element subsets of $[h]$, with opposite-class vertices adjacent when the corresponding subsets are disjoint. For every prime $h>3$ with $h\\equiv3\\pmod8$, we prove $$ γ(H(h,2))=1-\\frac{h(h-1)}{2} +\\frac{h(h-1)(h-2)(h-3)}{16}. $$ Euler's formula gives this lower bound, with equality for a quadrangulation. We construct a vertex-transitive orientable quadrangulation using an odd-order affine group that acts simply transitively on the two-element subsets. This gives an infinite family satisfying Pisanski's conjecture on quadrilateral embeddings of regular bipartite graphs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03159",
  "author_total": 2,
  "authors": [
    {
      "name": "Austin Ulrigg"
    },
    {
      "name": "Alexander Metzger"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/22m1aj87a6jd5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03159",
  "fulltext_url": null,
  "id": "22m1aj87a6jd5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03159",
  "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": "W7220383536",
  "pdf_url": "https://arxiv.org/pdf/2610.03159",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/22m1aj87a6jd5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.03159",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03159"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The Genus of Bipartite Kneser Graphs",
  "title_text": "The Genus of Bipartite Kneser Graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/22m1aj87a6jd5",
  "venue": "arXiv",
  "versions": []
}