{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:EVMMRDTSF742NKSDL4YVWVP2VV","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":"c685d645a74e157cd75a9f10f4ce148cdb541cf86e57c183a650cc9e0e3b9ca0","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-02-20T18:33:11Z","title_canon_sha256":"89f06ff851c3e3cebb93d14c28ae71a7522c972a538f833090482e81bc551ac4"},"schema_version":"1.0","source":{"id":"1702.06095","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.06095","created_at":"2026-05-17T23:43:54Z"},{"alias_kind":"arxiv_version","alias_value":"1702.06095v3","created_at":"2026-05-17T23:43:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.06095","created_at":"2026-05-17T23:43:54Z"},{"alias_kind":"pith_short_12","alias_value":"EVMMRDTSF742","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EVMMRDTSF742NKSD","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EVMMRDTS","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:81322d523b074cf9335e707ed604fe2620545e9cdd593bd1191ff6445143c461","target":"graph","created_at":"2026-05-17T23:43:54Z","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":"In this paper, we prove that, given a clique-width $k$-expression of an $n$-vertex graph, \\textsc{Hamiltonian Cycle} can be solved in time $n^{\\mathcal{O}(k)}$. This improves the naive algorithm that runs in time $n^{\\mathcal{O}(k^2)}$ by Espelage et al. (WG 2001), and it also matches with the lower bound result by Fomin et al. that, unless the Exponential Time Hypothesis fails, there is no algorithm running in time $n^{o(k)}$ (SIAM. J. Computing 2014).\n  We present a technique of representative sets using two-edge colored multigraphs on $k$ vertices. The essential idea is that, for a two-edge","authors_text":"Benjamin Bergougnoux, Mamadou Moustapha Kant\\'e, O-joung Kwon","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-02-20T18:33:11Z","title":"An optimal XP algorithm for Hamiltonian cycle on graphs of bounded clique-width"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.06095","kind":"arxiv","version":3},"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:f86f8c45a662fe4060632a589d200bcba9aab6c23047b4dcbff058999cf7f9fe","target":"record","created_at":"2026-05-17T23:43:54Z","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":"c685d645a74e157cd75a9f10f4ce148cdb541cf86e57c183a650cc9e0e3b9ca0","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-02-20T18:33:11Z","title_canon_sha256":"89f06ff851c3e3cebb93d14c28ae71a7522c972a538f833090482e81bc551ac4"},"schema_version":"1.0","source":{"id":"1702.06095","kind":"arxiv","version":3}},"canonical_sha256":"2558c88e722ff9a6aa435f315b55faad6846444370984b54ba49f40188c8af75","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2558c88e722ff9a6aa435f315b55faad6846444370984b54ba49f40188c8af75","first_computed_at":"2026-05-17T23:43:54.273157Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:54.273157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kIFgnbN7Ot3rPRBwxzOS29OxFWoMSan0/olF1Fdud7o3mejo006/yVIgbHpBAPoHbWHDEeR10av9gEvvvtFeAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:54.273809Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.06095","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f86f8c45a662fe4060632a589d200bcba9aab6c23047b4dcbff058999cf7f9fe","sha256:81322d523b074cf9335e707ed604fe2620545e9cdd593bd1191ff6445143c461"],"state_sha256":"9040ce33b5a2c694cd5d041f1347828bb918d9477758de69d5abfdf09fd468ae"}