{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:3I4AK2B4VJJDWYBNFRLUNRJL2K","short_pith_number":"pith:3I4AK2B4","schema_version":"1.0","canonical_sha256":"da3805683caa523b602d2c5746c52bd281e0fa7e4c89c8175bde508b97ab6841","source":{"kind":"arxiv","id":"cs/0702043","version":1},"attestation_state":"computed","paper":{"title":"Deciding k-colourability of $P_5$-free graphs in polynomial time","license":"","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Ch\\'inh T. Ho\\`ang, J. Sawada, Marcin Kami\\'nski, Vadim Lozin, X. Shu","submitted_at":"2007-02-07T15:29:32Z","abstract_excerpt":"The problem of computing the chromatic number of a $P_5$-free graph is known to be NP-hard. In contrast to this negative result, we show that determining whether or not a $P_5$-free graph admits a $k$-colouring, for each fixed number of colours $k$, can be done in polynomial time. If such a colouring exists, our algorithm produces it."},"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":"cs/0702043","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cs.DS","submitted_at":"2007-02-07T15:29:32Z","cross_cats_sorted":[],"title_canon_sha256":"84a707a5d1968f0eef0ac102da417eb2bff1cb93975de1192038da5b0a42b1de","abstract_canon_sha256":"9f2bb8b38de329ec08d29380be1b120dc99b3489df3525fdfa64f2fc4e6a1315"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:19.580680Z","signature_b64":"I/EL6qKnBkeZ9/hW2KwJws9amHcEr0UzMmbk3kcMjiLL+YrTedamsv1Er9rB+Ipj4qi3YQ3QoC+J76NJ6a0GAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da3805683caa523b602d2c5746c52bd281e0fa7e4c89c8175bde508b97ab6841","last_reissued_at":"2026-05-18T01:09:19.580172Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:19.580172Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Deciding k-colourability of $P_5$-free graphs in polynomial time","license":"","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Ch\\'inh T. Ho\\`ang, J. Sawada, Marcin Kami\\'nski, Vadim Lozin, X. Shu","submitted_at":"2007-02-07T15:29:32Z","abstract_excerpt":"The problem of computing the chromatic number of a $P_5$-free graph is known to be NP-hard. In contrast to this negative result, we show that determining whether or not a $P_5$-free graph admits a $k$-colouring, for each fixed number of colours $k$, can be done in polynomial time. If such a colouring exists, our algorithm produces it."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0702043","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"cs/0702043","created_at":"2026-05-18T01:09:19.580247+00:00"},{"alias_kind":"arxiv_version","alias_value":"cs/0702043v1","created_at":"2026-05-18T01:09:19.580247+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cs/0702043","created_at":"2026-05-18T01:09:19.580247+00:00"},{"alias_kind":"pith_short_12","alias_value":"3I4AK2B4VJJD","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_16","alias_value":"3I4AK2B4VJJDWYBN","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_8","alias_value":"3I4AK2B4","created_at":"2026-05-18T12:25:54.717736+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3I4AK2B4VJJDWYBNFRLUNRJL2K","json":"https://pith.science/pith/3I4AK2B4VJJDWYBNFRLUNRJL2K.json","graph_json":"https://pith.science/api/pith-number/3I4AK2B4VJJDWYBNFRLUNRJL2K/graph.json","events_json":"https://pith.science/api/pith-number/3I4AK2B4VJJDWYBNFRLUNRJL2K/events.json","paper":"https://pith.science/paper/3I4AK2B4"},"agent_actions":{"view_html":"https://pith.science/pith/3I4AK2B4VJJDWYBNFRLUNRJL2K","download_json":"https://pith.science/pith/3I4AK2B4VJJDWYBNFRLUNRJL2K.json","view_paper":"https://pith.science/paper/3I4AK2B4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=cs/0702043&json=true","fetch_graph":"https://pith.science/api/pith-number/3I4AK2B4VJJDWYBNFRLUNRJL2K/graph.json","fetch_events":"https://pith.science/api/pith-number/3I4AK2B4VJJDWYBNFRLUNRJL2K/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3I4AK2B4VJJDWYBNFRLUNRJL2K/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3I4AK2B4VJJDWYBNFRLUNRJL2K/action/storage_attestation","attest_author":"https://pith.science/pith/3I4AK2B4VJJDWYBNFRLUNRJL2K/action/author_attestation","sign_citation":"https://pith.science/pith/3I4AK2B4VJJDWYBNFRLUNRJL2K/action/citation_signature","submit_replication":"https://pith.science/pith/3I4AK2B4VJJDWYBNFRLUNRJL2K/action/replication_record"}},"created_at":"2026-05-18T01:09:19.580247+00:00","updated_at":"2026-05-18T01:09:19.580247+00:00"}