{
  "abstract": "The bipartite Turán number of a graph $H$, denoted $\\text{ex}(m, n; H)$, is the maximum number of edges in any $H$-free bipartite graph $G = (A, B; E)$ with parts of size $|A| = m$ and $|B| = n$. We study this problem for two families. For a tree $T = T(r, s)$ with parts $R$ and $S$ of sizes $|R| = r \\le s = |S|$, we prove \\[ (r - 1) n \\;\\le\\; \\text{ex}(m, n; T(r, s)) \\;\\le\\; (r - 1) n + C(m,r,s) \\] for $n$ sufficiently large compared to $m$, $r$, and $s$, where $C(m,r,s)$ does not depend on $n$, determining the leading-order term exactly (with the star case $r = 1$ solved with an exact formula). For a star forest $F = \\bigcup_{i=1}^k S_{d_i}$ with $d_1 \\ge \\cdots \\ge d_k$, we determine the exact value $\\text{ex}(m, n; F) = (k - 1) n + (d_k - 1)(m - k + 1)$ for $n$ sufficiently large, and characterize the unique extremal graph.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.01873",
  "author_total": 1,
  "authors": [
    {
      "name": "Omid Khormali"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a5cj6nvyjfm09.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.01873",
  "fulltext_url": null,
  "id": "a5cj6nvyjfm09",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.01873",
  "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",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7172426886",
  "pdf_url": "https://arxiv.org/pdf/2608.01873",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a5cj6nvyjfm09.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2608.01873",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.01873"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Bipartite Turán Numbers of Trees and Star Forests",
  "title_text": "Bipartite Turán Numbers of Trees and Star Forests",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/a5cj6nvyjfm09",
  "venue": "arXiv",
  "versions": []
}