{
  "abstract": "A labeling of a connected graph $G$ on $n$ vertices is a bijection $c:V(G)\\to\\{1,\\dots,n\\}$; writing $c(u,v)=|c(u)-c(v)|$, a vertex $u$ is list-distance consistent if $d(u,v)<d(u,w)$ implies $c(u,v)\\le c(u,w)$ for all $v,w$. The maximum number of such vertices over all labelings is the list-distance consistency ldc$(G)$, introduced by Casselgren and Henricsson. We prove that in a tree, the consistent vertices of any labeling lie on a single path, along which the labels form a block of consecutive integers in increasing order (with respect to a suitable orientation of the path), no vertex off the path receiving a label from that block. We deduce that ldc equals $3$ for every complete $k$-ary tree except the binary tree of height two, and we determine ldc for all spiders.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03803",
  "author_total": 4,
  "authors": [
    {
      "name": "Fei-Huang Chang"
    },
    {
      "name": "Ma-Lian Chia"
    },
    {
      "name": "David Kuo"
    },
    {
      "name": "Guan-Ting Lai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fn46gcjtzj0a1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03803",
  "fulltext_url": null,
  "id": "fn46gcjtzj0a1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03803",
  "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",
      "1703|Graph Labeling and Dimension Problems"
    ]
  ],
  "openalex": "W7208755267",
  "pdf_url": "https://arxiv.org/pdf/2609.03803",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fn46gcjtzj0a1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2609.03803",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03803"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "List-distance consistent vertices in trees are confined to a path",
  "title_text": "List-distance consistent vertices in trees are confined to a path",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/fn46gcjtzj0a1",
  "venue": "arXiv",
  "versions": []
}