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If $G$ is $(K_1+(K_1\\cup K_2))$-free, then $G$ is fully cycle extendable if and only if $2\\delta(G)\\geq n(G)$. If $G$ is $\\{ K_1+K_1+\\bar{K}_3,K_1+P_4\\}$-free or $\\{ K_1+K_1+\\bar{K}_3,K_1+(K_1\\cup P_3)\\}$-free, then $G$ is fully cycle extendable. If $G$ is distinct from $K_1+K_1+\\bar{K}_3$ and"},"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":"1507.07486","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-27T17:15:33Z","cross_cats_sorted":[],"title_canon_sha256":"6a84da5b1b5fe011ef8590f08f68783b90c7c74288f11dd326cfda753995930a","abstract_canon_sha256":"9faeea48d006aefb0de2899c7591da90b0b3b3b0b445868cdc6dab2f94d5ac93"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:16.286399Z","signature_b64":"ZnVnbeJJ3ED65DspWTYWze++yIJQ6v2jfKnGUIl6dKRSMEZZmOZnmmFzwxIRQYL2o6zY2yPw3nCg2Dd5NhxoCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f0cde2d8e43fd34b74e0b65fd3df365a07efd2e6c92245fcb616e150490fd942","last_reissued_at":"2026-05-18T01:36:16.285925Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:16.285925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local Connectivity, Local Degree Conditions, some Forbidden Induced Subgraphs, and Cycle Extendability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Christoph Brause, Dieter Rautenbach, Ingo Schiermeyer","submitted_at":"2015-07-27T17:15:33Z","abstract_excerpt":"The research in the present paper was motivated by the conjecture of Ryj\\'{a}\\v{c}ek that every locally connected graph is weakly pancyclic.\n  For a connected locally connected graph $G$ of order at least $3$, our results are as follows: If $G$ is $(K_1+(K_1\\cup K_2))$-free, then $G$ is weakly pancyclic. If $G$ is $(K_1+(K_1\\cup K_2))$-free, then $G$ is fully cycle extendable if and only if $2\\delta(G)\\geq n(G)$. If $G$ is $\\{ K_1+K_1+\\bar{K}_3,K_1+P_4\\}$-free or $\\{ K_1+K_1+\\bar{K}_3,K_1+(K_1\\cup P_3)\\}$-free, then $G$ is fully cycle extendable. 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