{
  "abstract": "The independent set polytope, or stable set polytope, of a graph $G$ is the 0/1-polytope defined by the convex hull of the characteristic vectors of all independent sets of $G$. We present a simple algorithm for computing a Hamilton path on the independent set polytope of a given $n$-vertex graph $G$ with amortized delay $\\mathcal{O}(n)$. The independent sets are listed such that two consecutive sets differ either in removing a vertex, or adding a vertex and removing its neighbors from the independent set, i.e., the symmetric difference between two consecutive independent sets induces a star in $G$. As applications of this result, we obtain an algorithm to compute a Hamilton path on the matching polytope of an $m$-edge graph $G$ with worst-case delay $\\mathcal{O}(m)$, which lists all matchings of $G$ in such a way that the symmetric difference between two consecutive matchings is a path on at most three edges. Furthermore, we obtain an algorithm to compute a Hamilton path on the chain polytope and order polytope of an $n$-element poset $P$ with amortized delay $\\mathcal{O}(n)$, which lists all antichains of $P$ or all ideals of $P$, respectively, by star exchanges. Our algorithms are derived from the generic framework proposed by Merino and Mütze (FOCS'23+SICOMP'24) for computing Hamilton paths on arbitrary 0/1-polytopes, which uses a linear optimization procedure as a black box. Our algorithms bypass solving the computationally intractable maximum weight independent set problem by a simple and purely combinatorial greedy rule.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07304",
  "author_total": 4,
  "authors": [
    {
      "name": "Jean Cardinal"
    },
    {
      "name": "Pia Herkenrath"
    },
    {
      "name": "Torsten Mütze"
    },
    {
      "name": "Francesco Verciani"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/34e2g7bkyk8yq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07304",
  "fulltext_url": null,
  "id": "34e2g7bkyk8yq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07304",
  "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",
      "cs.DM"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "1703|Complexity and Algorithms in Graphs"
    ]
  ],
  "openalex": "W7212060886",
  "pdf_url": "https://arxiv.org/pdf/2609.07304",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/34e2g7bkyk8yq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2609.07304",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07304"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A simple algorithm for computing Hamilton paths on independent set polytopes",
  "title_text": "A simple algorithm for computing Hamilton paths on independent set polytopes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/34e2g7bkyk8yq",
  "venue": "arXiv",
  "versions": []
}