{"paper":{"title":"A refinement of theorems on vertex-disjoint chorded cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Elyse Yeager, Michael Santana, Theodore Molla","submitted_at":"2015-11-13T16:49:57Z","abstract_excerpt":"In 1963, Corr\\'adi and Hajnal settled a conjecture of Erd\\H{o}s by proving that, for all $k \\geq 1$, any graph $G$ with $|G| \\geq 3k$ and minimum degree at least $2k$ contains $k$ vertex-disjoint cycles. In 2008, Finkel proved that for all $k \\geq 1$, any graph $G$ with $|G| \\geq 4k$ and minimum degree at least $3k$ contains $k$ vertex-disjoint chorded cycles. Finkel's result was strengthened by Chiba, Fujita, Gao, and Li in 2010, who showed, among other results, that for all $k \\geq 1$, any graph $G$ with $|G| \\geq 4k$ and minimum Ore-degree at least $6k-1$ contains $k$ vertex-disjoint cycles"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.04356","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":""},"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"}