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Affif Chaouche, Rutherford, and Whitty introduced the function $c(n,k)$. They showed that for every integer $k \\geq 2$, $c(n , k ) \\geq \\Omega_k ( n^{1/k} )$ and they asked if $n^{1/k}$ gives the correct order of magnitude of $c(n, k)$ for $k \\geq 2$. Our main theorem answers this question as we prove t"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1612.08802","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-12-28T04:49:38Z","cross_cats_sorted":[],"title_canon_sha256":"f93e6a9c508a988b2c428e1798b3b84116c72079ec73b35922269bd4ca116efc","abstract_canon_sha256":"efcfe1efbf8a9a2f76c25f99a1db38db5620ced6be822850213c0ece928c4e6a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:56.025175Z","signature_b64":"Mx849p9W9pE4P1B8w10kIr5Y6jhttZY5xsQKjt6FUNw81RL8f7zS4Lmtm1Vyx95XrVLRq8qikrhlHDn+D1F5Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a18019945c295486ee240246a5dd92ad7a64061d49d689f5bda78ccb89c29590","last_reissued_at":"2026-05-18T00:31:56.024675Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:56.024675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pancyclicity when each cycle contains k chords","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Vladislav Taranchuk","submitted_at":"2016-12-28T04:49:38Z","abstract_excerpt":"For integers $n \\geq k \\geq 2$, let $c(n,k)$ be the minimum number of chords that must be added to a cycle of length $n$ so that the resulting graph has the property that for every $l \\in \\{ k , k + 1 , \\dots , n \\}$, there is a cycle of length $l$ that contains exactly $k$ of the added chords. Affif Chaouche, Rutherford, and Whitty introduced the function $c(n,k)$. They showed that for every integer $k \\geq 2$, $c(n , k ) \\geq \\Omega_k ( n^{1/k} )$ and they asked if $n^{1/k}$ gives the correct order of magnitude of $c(n, k)$ for $k \\geq 2$. 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