{"paper":{"title":"Induced even cycles in locally sparse graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bingyu Luan, Hong Liu, Jun Gao, Laihao Ding, Shumin Sun","submitted_at":"2024-11-19T17:07:29Z","abstract_excerpt":"A graph $G$ is $(c,t)$-sparse if for every pair of vertex subsets $A,B\\subset V(G)$ with $|A|,|B|\\geq t$, $e(A,B)\\leq (1-c)|A||B|$. In this paper we prove that for every $c>0$ and integer $\\ell$, there exists $C>1$ such that if an $n$-vertex graph $G$ is $(c,t)$-sparse for some $t$, and has at least $C t^{1-1/\\ell}n^{1+1/\\ell}$ edges, then $G$ contains an induced copy of $C_{2\\ell}$. This resolves a conjecture of Fox, Nenadov and Pham."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.12659","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/2411.12659/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"}