{"paper":{"title":"Many vertex-disjoint even cycles of fixed length in a graph","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Caihong Yang, Caiyun Hu, Heng Li, Jianfeng Hou, Xizhi Liu, Yixiao Zhang","submitted_at":"2023-11-26T02:25:23Z","abstract_excerpt":"For every integer $k \\ge 3$, we determine the extremal structure of an $n$-vertex graph with at most $t$ vertex-disjoint copies of $C_{2k}$ when $n$ is sufficiently large and $t$ lies in the interval $\\left[\\frac{\\mathrm{ex}(n,C_{2k})}{\\varepsilon n}, \\varepsilon n\\right]$, where $\\varepsilon>0$ is a constant depending only on $k$. The question for $k = 2$ and $t = o\\left(\\frac{\\mathrm{ex}(n,C_{2k})}{n}\\right)$ was explored in prior work~\\cite{HHLLYZ23a}, revealing different extremal structures in these cases. Our result can be viewed as an extension of the theorems by Egawa~\\cite{Ega96} and V"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.16189","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2311.16189/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}