{
  "abstract": "Let $r\\geq 2$ be an integer. An $r$-partite graph $Γ$ with vertex partition $V_1,\\ldots,V_r$ is $2$-balanced if there exists a positive integer $n$ such that $n\\leq |V_i|\\leq 2n$ for every $i\\in[r]$. For an integer $\\ell\\geq3$, let $C_\\ell$ denote the cycle of length $\\ell$, and define $\\hatδ(Γ)=\\min\\{d_Γ(v,V_i)/|V_i|:i\\in[r],\\ v\\in V(Γ)\\setminus V_i\\}$. Let $\\hatδ^r_{C_\\ell}$ denote the $C_\\ell$-decomposition threshold for $2$-balanced $r$-partite graphs, that is, the least nonnegative real number $δ$ such that, for every $\\varepsilon>0$, there exists $n_0$ such that every $C_\\ell$-divisible $2$-balanced $r$-partite graph $G$ with $\\min_i|V_i|>n_0$ and $\\hatδ(G)\\geqδ+\\varepsilon$ admits a $C_\\ell$-decomposition. We prove that $\\hatδ^{r}_{C_4}=\\frac{2}{3}$ and $\\hatδ^{r}_{C_{2k}}=\\frac{1}{2}$ for every $r\\geq2$ and every $k\\geq3$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04890",
  "author_total": 3,
  "authors": [
    {
      "name": "Weiyi Sun"
    },
    {
      "name": "Tao Feng"
    },
    {
      "name": "Shikang Yu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/edv2gp7y0xxnj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04890",
  "fulltext_url": null,
  "id": "edv2gp7y0xxnj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04890",
  "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": "W7220683459",
  "pdf_url": "https://arxiv.org/pdf/2610.04890",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/edv2gp7y0xxnj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.04890",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04890"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Even cycle decomposition thresholds for dense multipartite graphs",
  "title_text": "Even cycle decomposition thresholds for dense multipartite graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/edv2gp7y0xxnj",
  "venue": "arXiv",
  "versions": []
}