{
  "abstract": "We characterize tree-child phylogenetic networks in terms of their mu-representations. First, we give a structural characterization of tree-child networks by means of ordered tree-path decompositions. We then translate this decomposition into a set of purely vectorial conditions on finite subsets M in N^n. We prove that such a set M is the mu-representation of a tree-child phylogenetic network if and only if it is tree-child mu-compatible. This provides a feasibility criterion for tree-child mu-representations which can be used as a basis for reconstruction and further algorithmic applications. Note that this paper presents results arising from ongoing research on tree-child networks and that the results will be further developed and placed into proper context in subsequent versions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25177",
  "author_total": 4,
  "authors": [
    {
      "name": "Toni Fuentes"
    },
    {
      "name": "Vincent Moulton"
    },
    {
      "name": "Katharina T. Huber"
    },
    {
      "name": "Joan Carles Pons"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b9azxeqst69s5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25177",
  "fulltext_url": null,
  "id": "b9azxeqst69s5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25177",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "q-bio.PE"
    ],
    [
      "openalex",
      "1312|Genomics and Phylogenetic Studies"
    ]
  ],
  "openalex": "W7214072473",
  "pdf_url": "https://arxiv.org/pdf/2609.25177",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b9azxeqst69s5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.25177",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25177"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "arxiv:q-bio.PE",
      "subfield": "evolutionary-biology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Characterization of tree-child networks in terms of mu vectors",
  "title_text": "Characterization of tree-child networks in terms of mu vectors",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:44Z",
  "url": "https://research.draconitic.com/paper/b9azxeqst69s5",
  "venue": "arXiv",
  "versions": []
}