{
  "abstract": "It has been conjectured that $χ_{\\mathrm{la}}(T)\\leq\\ell(T)+2$ for every tree $T$ of order at least three, where $χ_{\\mathrm{la}}(T)$ is the local antimagic chromatic number and $\\ell(T)$ denotes the number of leaves. We disprove this bound and show that no absolute constant can replace $2$ in an inequality of this form. Our approach uses degree-based intervals containing all possible induced vertex weights under bijective edge labelings, together with a separation criterion that forces selected internal vertex weights to be distinct. We first construct caterpillars $T_3$ and $T_4$ satisfying $χ_{\\mathrm{la}}(T_3)=\\ell(T_3)+3$ and $χ_{\\mathrm{la}}(T_4)=\\ell(T_4)+4$, respectively. We then construct, for every positive integer $r$, infinitely many pairwise nonisomorphic caterpillars with exactly $r$ internal vertices for which every bijective edge labeling is antimagic. Each such caterpillar $T$ satisfies $χ_{\\mathrm{la}}(T)=|V(T)|=\\ell(T)+r$. Consequently, $χ_{\\mathrm{la}}(T)-\\ell(T)$ is unbounded even within the class of caterpillars, and no absolute constant $C$ can satisfy $χ_{\\mathrm{la}}(T)\\leq\\ell(T)+C$ for every tree $T$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.22783",
  "author_total": 2,
  "authors": [
    {
      "name": "André Ebling Brondani"
    },
    {
      "name": "Francisca Andrea Macedo França"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/120q7b02dqb73.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.22783",
  "fulltext_url": null,
  "id": "120q7b02dqb73",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.22783",
  "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|Graph Labeling and Dimension Problems"
    ]
  ],
  "openalex": "W7222952110",
  "pdf_url": "https://arxiv.org/pdf/2610.22783",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/120q7b02dqb73.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.22783",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.22783"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Counterexamples to the local antimagic leaf conjecture",
  "title_text": "Counterexamples to the local antimagic leaf conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/120q7b02dqb73",
  "venue": "arXiv",
  "versions": []
}