{
  "abstract": "The bipartite edge frustration of a graph $G$, $φ(G)$, is the minimum number of edges that must be removed from $G$ to obtain a graph that is bipartite. Core graphs are singular graphs on $2$ or more vertices, for which the kernel of the adjacency matrix contains a full eigenvector. A nut graph is a core graph of nullity one. Nut graphs $G$ are non-bipartite. It is proved here that $φ(G) \\geq 2$ if $G$ is a nut graph, i.e. every nut graph requires deletion of at least two edges to produce a bipartite graph. In addition, we give a constructive proof that for every integer $k \\geq 2$ there exist infinitely many chemical nut graphs $G$ with $φ(G) = k$. Furthermore, for $3 \\leq d \\leq 8$, the values $k$, for which a $d$-regular nut graph $G$ with $φ(G) = k$ exists, are characterised. It is shown here that for every integer $k \\geq 2$ there exist infinitely many cubic polyhedral nut graphs $G$ with $φ(G) = k$. Two ways of producing larger nut graphs from smaller are described: the cut and frustration constructions. One straightforward consequence is that total double subdivision of a nut graph (i.e. simultaneous insertion of two degree-$2$ vertices into every edge) yields a nut graph.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15679",
  "author_total": 2,
  "authors": [
    {
      "name": "Nino Bašić"
    },
    {
      "name": "Patrick W. Fowler"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9y07kt536ajq6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15679",
  "fulltext_url": null,
  "id": "9y07kt536ajq6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15679",
  "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",
      "2608|Graph theory and applications"
    ]
  ],
  "openalex": "W7221791319",
  "pdf_url": "https://arxiv.org/pdf/2610.15679",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9y07kt536ajq6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15679",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15679"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Bipartite edge frustration of nut graphs: proofs and constructions",
  "title_text": "Bipartite edge frustration of nut graphs: proofs and constructions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/9y07kt536ajq6",
  "venue": "arXiv",
  "versions": []
}