{
  "abstract": "We bound fractional chromatic numbers by establishing a connection with low-weight odd-cycle transversals. Let $\\ell\\geq 3$ be an integer and let $G$ be a graph of odd girth at least $\\ell$ whose odd-cycle covering polyhedron is integral. For every nonnegative weight vector $w=(w_v)_{v\\in V(G)}\\in \\mathbb{R}_{\\geq 0}^{V(G)}$, we obtain a set $Z\\subseteq V(G)$ such that $G-Z$ is bipartite and $w(Z)\\leq\\frac{mad(G)}{2\\ell}w(V(G))$. Here, $w(S)=\\sum_{v\\in S}w_v$ for any $S\\subseteq V(G)$, and $mad(G)$ denotes the maximum average degree of $G$. Consequently, if $mad(G)<2\\ell$, then $G$ has fractional chromatic number at most $\\frac{4\\ell}{2\\ell-mad(G)}$. As applications, we prove that, for every positive integer $k$, every $n$-vertex planar graph of girth at least $2k+3$ has fractional chromatic number at most $\\frac{2k+1}{k}(1-\\frac{1}{kn+1})$, establishing the girth version of Naserasr's fractional coloring conjecture with a strict inequality. For $k=1$, we furthermore prove that the upper bound $\\frac{3n}{n+1}$ holds for every $n$-vertex triangle-free planar graph and this is attained for infinitely many values of $n$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30719",
  "author_total": 3,
  "authors": [
    {
      "name": "Xiaolan Hu"
    },
    {
      "name": "Jiaao Li"
    },
    {
      "name": "Zhouningxin Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ar2qkaqsedy11.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30719",
  "fulltext_url": null,
  "id": "ar2qkaqsedy11",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30719",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7223358472",
  "pdf_url": "https://arxiv.org/pdf/2610.30719",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ar2qkaqsedy11.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.30719",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30719"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Weighted odd-cycle transversals and fractional colorings of planar graphs",
  "title_text": "Weighted odd-cycle transversals and fractional colorings of planar graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/ar2qkaqsedy11",
  "venue": "arXiv",
  "versions": []
}