{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:V6RNSRMI5S6L2OVPLCIYNJEOGQ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"c29a11066063ac5c06b91055fb05293d840a4acc349d9375777e17a383b0ac65","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-12-03T20:15:43Z","title_canon_sha256":"85c5d97a2eb230f7758434ea93b54a51578a49ed6aa310c1d19201ef73cc044e"},"schema_version":"1.0","source":{"id":"1712.00831","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.00831","created_at":"2026-05-18T00:29:00Z"},{"alias_kind":"arxiv_version","alias_value":"1712.00831v1","created_at":"2026-05-18T00:29:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.00831","created_at":"2026-05-18T00:29:00Z"},{"alias_kind":"pith_short_12","alias_value":"V6RNSRMI5S6L","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"V6RNSRMI5S6L2OVP","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"V6RNSRMI","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:39b952369dac3e66a333a939c96a172076e2e1cf64ee8182d8b792f1e83c4345","target":"graph","created_at":"2026-05-18T00:29:00Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The investigation of conditions guaranteeing the appearance of cycles of certain lengths is one of the most well-studied topics in graph theory. In this paper we consider a problem of this type which asks, for fixed integers ${\\ell}$ and $k$, how many copies of the $k$-cycle guarantee the appearance of an $\\ell$-cycle? Extending previous results of Bollob\\'as--Gy\\H{o}ri--Li and Alon--Shikhelman, we fully resolve this problem by giving tight (or nearly tight) bounds for all values of $\\ell$ and $k$.\n  We also present a somewhat surprising application of the above mentioned estimates to the stud","authors_text":"Asaf Shapira, Lior Gishboliner","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-12-03T20:15:43Z","title":"A Generalized Tur\\'an Problem and its Applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00831","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c9d4cca1b64d2296e059ba4f50104d6b233afd0d55c38d57f98834498fac0031","target":"record","created_at":"2026-05-18T00:29:00Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"c29a11066063ac5c06b91055fb05293d840a4acc349d9375777e17a383b0ac65","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-12-03T20:15:43Z","title_canon_sha256":"85c5d97a2eb230f7758434ea93b54a51578a49ed6aa310c1d19201ef73cc044e"},"schema_version":"1.0","source":{"id":"1712.00831","kind":"arxiv","version":1}},"canonical_sha256":"afa2d94588ecbcbd3aaf589186a48e34194ff8030dfe91f1b93e69653b20f9ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"afa2d94588ecbcbd3aaf589186a48e34194ff8030dfe91f1b93e69653b20f9ce","first_computed_at":"2026-05-18T00:29:00.287681Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:00.287681Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gknkRBeYLdEmeYkHNi2+nFBFo0jJuDhNze07NWrc6zsRS/c4eGQFBpdc4BLCjGmL/5YpjF2wFNQo85U0j7QBCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:00.288197Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.00831","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c9d4cca1b64d2296e059ba4f50104d6b233afd0d55c38d57f98834498fac0031","sha256:39b952369dac3e66a333a939c96a172076e2e1cf64ee8182d8b792f1e83c4345"],"state_sha256":"e155aa6dbb847a7547bcec595c8fee4aa01a64d2de6a0a44e7d8d8ad955d6fd2"}