{"paper":{"title":"Cycle lengths in graphs of given minimum degree","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrzej Grzesik, Binlong Li, Magdalena Prorok, Yandong Bai","submitted_at":"2025-11-05T00:21:31Z","abstract_excerpt":"We prove that if $G$ is a 2-connected graph with minimum degree at least $k\\geqslant 4$, then\n  (1) $G$ contains $k$ cycles whose lengths form an arithmetic progression with common difference one or two, unless $G\\cong K_{k+1}$ or $K_{k,n-k}$;\n  (2) $G$ contains cycles of lengths $\\ell$ modulo $k$ for all even $\\ell$, unless $G\\cong K_{k+1}$ or $K_{k,n-k}$;\n  (3) $G$ contains cycles of lengths $\\ell$ modulo $k$ for all $\\ell$, unless $G\\cong K_{k+1}$ or $G$ is bipartite.\n  In addition, we show that if $k$ is even and $G$ is 2-connected with minimum degree at least $k-1$ and order at least $k+2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.03085","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/2511.03085/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"}