{"paper":{"title":"Minimal Pancyclicity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Sean Griffin","submitted_at":"2013-12-01T21:01:09Z","abstract_excerpt":"A pancyclic graph is a simple graph containing a cycle of length $k$ for all $3\\leq k\\leq n$. Let $m(n)$ be the minimum number of edges of all pancyclic graphs on $n$ vertices. Exact values are given for $m(n)$ for $n\\leq 37$, combining calculations from an exhaustive search on graphs with up to 29 vertices with a construction that works for up to 37 vertices. The behavior of $m(n)$ in general is also explored, including a proof of the conjecture that $m(n+1)>m(n)$ for all $n$ in some special cases."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0274","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"}