{
  "abstract": "We give a deterministic algorithm for minimum-cost Hamiltonian cycle in undirected graphs with arbitrary real edge costs and an independent set of size at least $αn$, for any fixed $3/7<α\\le1/2$. It runs in $O^*(γ(α)^n)$ time for an explicit constant $γ(α)<2$; for bipartite graphs, the bound is $O^*((1+2\\sqrt2)^{n/2})\\approx O^*(1.957^n)$. The algorithm is based on a restricted Held--Karp dynamic program. Its state enumeration uses structural properties of minimum-cost assignments arising from a regular triangulation of a product of simplices.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41178",
  "author_total": 4,
  "authors": [
    {
      "name": "Ethan X. Fang"
    },
    {
      "name": "Shengtao Guo"
    },
    {
      "name": "Junwei Lu"
    },
    {
      "name": "Yuan Yao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5gdm7w173q7rm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41178",
  "fulltext_url": null,
  "id": "5gdm7w173q7rm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.41178",
  "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",
      "cs.DS"
    ],
    [
      "arxiv",
      "math.CO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.41178",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5gdm7w173q7rm.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.41178",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41178"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Traveling Salesman Problem on Graphs with Proportional Independent Set",
  "title_text": "Traveling Salesman Problem on Graphs with Proportional Independent Set",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:52Z",
  "url": "https://research.draconitic.com/paper/5gdm7w173q7rm",
  "venue": "arXiv",
  "versions": []
}