{"paper":{"title":"A strengthening on consecutive odd cycles in graphs of given minimum degree","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Guanghui Wang, Hao Lin, Wenling Zhou","submitted_at":"2024-10-01T13:01:17Z","abstract_excerpt":"Liu and Ma [J. Combin. Theory Ser. B, 2018] conjectured that every $2$-connected non-bipartite graph with minimum degree at least $k+1$ contains $\\lceil k/2\\rceil $ cycles with consecutive odd lengths. In particular, they showed that this conjecture holds when $k$ is even. In this paper, we confirm this conjecture for any $k\\in \\mathbb N$. Moreover, we also improve some previous results about cycles of consecutive lengths."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.00648","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/2410.00648/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"}