{"paper":{"title":"Cycle lengths in expanding graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Limor Friedman, Michael Krivelevich","submitted_at":"2019-12-23T18:14:10Z","abstract_excerpt":"For a positive constant $\\alpha$ a graph $G$ on $n$ vertices is called an $\\alpha$-expander if every vertex set $U$ of size at most $n/2$ has an external neighborhood whose size is at least $\\alpha\\left|U\\right|$. We study cycle lengths in expanding graphs. We first prove that cycle lengths in $\\alpha$-expanders are well distributed. Specifically, we show that for every $0<\\alpha\\leq1$ there exist positive constants $n_{0}$, $C$ and $A=O(1/\\alpha)$ such that for every $\\alpha$-expander $G$ on $n\\geq n_{0}$ vertices and every integer $\\ell\\in\\left[C\\log n,\\frac{n}{C}\\right]$, $G$ contains a cyc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.11011","kind":"arxiv","version":2},"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/1912.11011/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"}