{
  "abstract": "A signed graph $(G,σ)$ is a graph $G$ with a signature $σ$ labeling each edge with a positive or negative sign. Two signatures of $G$ are switching equivalent if one is obtained from the other by sequentially changing the signs of all edges in an edge-cut. The frustration index of a signed graph $(G, σ)$ is the minimum number of negative edges among all signatures switching equivalent to $σ$. A signed graph is critically $k$-frustrated if it has frustration index $k$, and the removal of any edge decreases its frustration index. A critically $k$-frustrated signed graph is prime if it is irreducible and contains no two edge-disjoint negative cycles. Steffen and Naserasr et al. asked if there are only finitely many prime critically $k$-frustrated signed graphs for any positive integer $k$. The cases $k\\leq 3$ were proved to be true by Cappello et al., and later, the cases $k=4$ and $5$ were verified by Z. Wang. In this paper, the author proves the conjecture by a topological argument.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06017",
  "author_total": 1,
  "authors": [
    {
      "name": "Zhiqian Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1j0eafwvd7jr6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06017",
  "fulltext_url": null,
  "id": "1j0eafwvd7jr6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06017",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06017",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1j0eafwvd7jr6.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.06017",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06017"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Finiteness of Non-decomposable Critically Frustrated Signed Graphs",
  "title_text": "Finiteness of Non-decomposable Critically Frustrated Signed Graphs",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:30Z",
  "url": "https://research.draconitic.com/paper/1j0eafwvd7jr6",
  "venue": "arXiv",
  "versions": []
}