{"paper":{"title":"Pancyclicity when each cycle must pass exactly $k$ Hamilton cycle chords","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Carrie Rutherford, Fatima Affif Chaouche, Robin Whitty","submitted_at":"2012-12-14T23:27:36Z","abstract_excerpt":"It is known that $\\Theta(\\log n)$ chords must be added to an $n$-cycle to produce a pancyclic graph; for vertex pancyclicity, where every vertex belongs to a cycle of every length, $\\Theta(n)$ chords are required. A possibly `intermediate' variation is the following: given $k$, $1\\leq k\\leq n$, how many chords must be added to ensure that there exist cycles of every length each of which passes exactly $k$ chords? For fixed $k$, we establish a lower bound of $\\Omega\\big(n^{1/k}\\big)$ on the growth rate."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.3633","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":""},"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"}