{
  "abstract": "For every $α\\ge3$ and all sufficiently large $n$, we identify a single graph that simultaneously maximizes the number of independent sets of every size among all $n$-vertex $2$-connected graphs with independence number $α$. This graph is unique up to isomorphism and is a balanced cycle-linking of the disjoint union of $α$ cliques whose orders differ by at most one. More precisely, for each $3\\leβ\\leα$, the graphs maximizing the number of independent $β$-sets are exactly the cycle-linkings whose clique-size cyclic words are $\\lfloorβ/2\\rfloor$-balanced. These results extend the corresponding extremal result for connected graphs to the $2$-connected setting. The proof combines generalized Turán-type clique counting and the edge-extremal theory of $2$-connected graphs with a coefficientwise balancing-switch argument. The switch also shows that a shortest imbalance of length $r$ first affects the independent-set count in degree $2r$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15637",
  "author_total": 1,
  "authors": [
    {
      "name": "Shuaichao Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9gab5p4sc9hf9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15637",
  "fulltext_url": null,
  "id": "9gab5p4sc9hf9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15637",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7213309779",
  "pdf_url": "https://arxiv.org/pdf/2609.15637",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9gab5p4sc9hf9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.15637",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15637"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Independent Sets and Balanced Cycle-Linkings in 2-Connected Graphs",
  "title_text": "Independent Sets and Balanced Cycle-Linkings in 2-Connected Graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/9gab5p4sc9hf9",
  "venue": "arXiv",
  "versions": []
}