{
  "abstract": "Let $G$ be a graph and $S\\subseteq V(G)$ be a subset of vertices. An $S$-Steiner tree $T$ of $G$ is a tree of $G$ which contains $S$ in its vertex set $V(T)$. Kriesell conjectured that for every $2k$-edge-connected subset $S\\subseteq V(G)$ in a finite connected graph $G$, there exist $k$ pairwise edge-disjoint $S$-Steiner trees. This conjecture is false for infinite graphs. We present a version of Kriesell's conjecture with topological $S$-Steiner trees for countable finitely edge-separable graphs and a version with $F$-limits of trees for rayless graphs. We show that if Kriesell's conjecture holds for finite graphs, then it holds for every connected, rayless and finitely edge-separable graph. We also show that every $2k$-edge-connected rayless and finitely edge-separable graph contains $k$ pairwise edge-disjoint spanning trees.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11534",
  "author_total": 3,
  "authors": [
    {
      "name": "Leandro Aurichi"
    },
    {
      "name": "Paulo Magalhães Júnior"
    },
    {
      "name": "Rodrigo Santos Monteiro"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ehdgwhn5qwg83.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11534",
  "fulltext_url": null,
  "id": "ehdgwhn5qwg83",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11534",
  "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",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7212314948",
  "pdf_url": "https://arxiv.org/pdf/2609.11534",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ehdgwhn5qwg83.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.11534",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11534"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Kriesell's conjecture for infinite graphs",
  "title_text": "Kriesell's conjecture for infinite graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/ehdgwhn5qwg83",
  "venue": "arXiv",
  "versions": []
}