{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:DSQ7AVJYQNGTIUACO3TBJVOPSS","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":"6c41a540d27f158100ad19762a256acaffe2bd24118153110daf13929ac56316","cross_cats_sorted":["cs.CC","cs.DM","cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-12T11:43:40Z","title_canon_sha256":"d92a9b87ec7a8b1795d11689e227ae0c94bfb2445662cbaab35849927fd85b1e"},"schema_version":"1.0","source":{"id":"1412.3955","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.3955","created_at":"2026-05-18T01:22:08Z"},{"alias_kind":"arxiv_version","alias_value":"1412.3955v2","created_at":"2026-05-18T01:22:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.3955","created_at":"2026-05-18T01:22:08Z"},{"alias_kind":"pith_short_12","alias_value":"DSQ7AVJYQNGT","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DSQ7AVJYQNGTIUAC","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DSQ7AVJY","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:d0b11c0170c9c7d9992c724ec84202ba4c8e798c77570edd4b998a3e9353b84b","target":"graph","created_at":"2026-05-18T01:22:08Z","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 cyclability of a graph is the maximum integer $k$ for which every $k$ vertices lie on a cycle. The algorithmic version of the problem, given a graph $G$ and a non-negative integer $k,$ decide whether the cyclability of $G$ is at least $k,$ is {\\sf NP}-hard. We study the parametrized complexity of this problem. We prove that this problem, parameterized by $k,$ is ${\\sf co\\mbox{-}W[1]}$-hard and that its does not admit a polynomial kernel on planar graphs, unless ${\\sf NP}\\subseteq{\\sf co}\\mbox{-}{\\sf NP}/{\\sf poly}$. On the positive side, we give an {\\sf FPT} algorithm for planar graphs tha","authors_text":"Dimitrios M. Thilikos, Marcin Kami\\'nski, Petr A. Golovach, Spyridon Maniatis","cross_cats":["cs.CC","cs.DM","cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-12T11:43:40Z","title":"The Parameterized Complexity of Graph Cyclability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3955","kind":"arxiv","version":2},"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":"sha256:8e6224e4f20360a3dfad633cb1e0c7373a72e3eeaae7df339350078b150b99d2","target":"record","created_at":"2026-05-18T01:22:08Z","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":"6c41a540d27f158100ad19762a256acaffe2bd24118153110daf13929ac56316","cross_cats_sorted":["cs.CC","cs.DM","cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-12T11:43:40Z","title_canon_sha256":"d92a9b87ec7a8b1795d11689e227ae0c94bfb2445662cbaab35849927fd85b1e"},"schema_version":"1.0","source":{"id":"1412.3955","kind":"arxiv","version":2}},"canonical_sha256":"1ca1f05538834d34500276e614d5cf94ac505e94e0315f7e05f399db7589766e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ca1f05538834d34500276e614d5cf94ac505e94e0315f7e05f399db7589766e","first_computed_at":"2026-05-18T01:22:08.306786Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:08.306786Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cN6q0xp7xemmhsun5CskOJGMZm63CCwsgGlIBm3y41BpY9CG+kdBpsfV59cSjmaTk0gIFn9IKofGG43QYCsNBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:08.307473Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.3955","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8e6224e4f20360a3dfad633cb1e0c7373a72e3eeaae7df339350078b150b99d2","sha256:d0b11c0170c9c7d9992c724ec84202ba4c8e798c77570edd4b998a3e9353b84b"],"state_sha256":"fe9d1da3f9b21187246854fa57137c88eea692818b6e98dcb42eb6532874e018"}