{
  "abstract": "We construct near-spanning balanced antidirected trees that fail to embed in highly symmetric tournaments despite the conjectured semidegree condition being satisfied. More precisely, for every sufficiently large odd integer $n$, we exhibit a regular vertex-transitive tournament on $n$ vertices and a balanced antidirected caterpillar on $n-1$ vertices with maximum degree at most $(1+o(1))n/\\log_2 n$ that is not contained in the tournament. The host satisfies the strict $k/2$ threshold in both the semidegree and pseudo-semidegree settings, where $k$ is the number of arcs of the target tree. Consequently, this gives counterexamples to the uniform sublinear-degree interpretations of Conjectures~6.8 and~7.6 in Stein's survey (2024). The order $n-1$ of the target is best possible under the strict semidegree hypothesis. We also give a six-vertex balanced antidirected double-star missing from the seven-vertex Paley tournament, and show that seven is the smallest host order for a pseudo-semidegree counterexample with this fixed double-star.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02390",
  "author_total": 2,
  "authors": [
    {
      "name": "Gregory Gutin"
    },
    {
      "name": "Yiming Hao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/baq71jtesrfy2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02390",
  "fulltext_url": null,
  "id": "baq71jtesrfy2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02390",
  "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",
      "cs.DM"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7220403633",
  "pdf_url": "https://arxiv.org/pdf/2610.02390",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/baq71jtesrfy2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.02390",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02390"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Note on near-spanning balanced antidirected trees missing from regular tournaments",
  "title_text": "Note on near-spanning balanced antidirected trees missing from regular tournaments",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/baq71jtesrfy2",
  "venue": "arXiv",
  "versions": []
}