{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:JROGOWEXMOOOL74QGCBVBEKTFO","short_pith_number":"pith:JROGOWEX","schema_version":"1.0","canonical_sha256":"4c5c675897639ce5ff9030835091532b8cd2260117e0947343cc47c2e7c0f747","source":{"kind":"arxiv","id":"1512.02207","version":1},"attestation_state":"computed","paper":{"title":"The complexity of partitioning into disjoint cliques and a triangle-free graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Marin Bougeret, Pascal Ochem","submitted_at":"2015-12-07T20:49:14Z","abstract_excerpt":"Motivated by Chudnovsky's structure theorem of bull-free graphs, Abu-Khzam, Feghali, and M\\\"uller have recently proved that deciding if a graph has a vertex partition into disjoint cliques and a triangle-free graph is NP-complete for five graph classes. The problem is trivial for the intersection of these five classes. We prove that the problem is NP-complete for the intersection of two subsets of size four among the five classes. We also show NP-completeness for other small classes, such as graphs with maximum degree 4 and line graphs."},"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":"1512.02207","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-12-07T20:49:14Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"f578b189006d9348f106565b977481d66e9565f51c85d1d32b824aa62bef2716","abstract_canon_sha256":"64ae9c9d37dd3bed059429cf758e749382517d5bd223e61abeb59c448064daee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:09.082033Z","signature_b64":"u+iZT5hZTrX3ac3tlNRuS8Rw4Y55OFj1W+Uws5kkf2/MVsGF131FLxt22kTwA3CL8IFvdiURs2eCyjiN9ZVeBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c5c675897639ce5ff9030835091532b8cd2260117e0947343cc47c2e7c0f747","last_reissued_at":"2026-05-18T01:25:09.081450Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:09.081450Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The complexity of partitioning into disjoint cliques and a triangle-free graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Marin Bougeret, Pascal Ochem","submitted_at":"2015-12-07T20:49:14Z","abstract_excerpt":"Motivated by Chudnovsky's structure theorem of bull-free graphs, Abu-Khzam, Feghali, and M\\\"uller have recently proved that deciding if a graph has a vertex partition into disjoint cliques and a triangle-free graph is NP-complete for five graph classes. The problem is trivial for the intersection of these five classes. We prove that the problem is NP-complete for the intersection of two subsets of size four among the five classes. We also show NP-completeness for other small classes, such as graphs with maximum degree 4 and line graphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02207","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":"1512.02207","created_at":"2026-05-18T01:25:09.081523+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.02207v1","created_at":"2026-05-18T01:25:09.081523+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.02207","created_at":"2026-05-18T01:25:09.081523+00:00"},{"alias_kind":"pith_short_12","alias_value":"JROGOWEXMOOO","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_16","alias_value":"JROGOWEXMOOOL74Q","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_8","alias_value":"JROGOWEX","created_at":"2026-05-18T12:29:27.538025+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/JROGOWEXMOOOL74QGCBVBEKTFO","json":"https://pith.science/pith/JROGOWEXMOOOL74QGCBVBEKTFO.json","graph_json":"https://pith.science/api/pith-number/JROGOWEXMOOOL74QGCBVBEKTFO/graph.json","events_json":"https://pith.science/api/pith-number/JROGOWEXMOOOL74QGCBVBEKTFO/events.json","paper":"https://pith.science/paper/JROGOWEX"},"agent_actions":{"view_html":"https://pith.science/pith/JROGOWEXMOOOL74QGCBVBEKTFO","download_json":"https://pith.science/pith/JROGOWEXMOOOL74QGCBVBEKTFO.json","view_paper":"https://pith.science/paper/JROGOWEX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.02207&json=true","fetch_graph":"https://pith.science/api/pith-number/JROGOWEXMOOOL74QGCBVBEKTFO/graph.json","fetch_events":"https://pith.science/api/pith-number/JROGOWEXMOOOL74QGCBVBEKTFO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JROGOWEXMOOOL74QGCBVBEKTFO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JROGOWEXMOOOL74QGCBVBEKTFO/action/storage_attestation","attest_author":"https://pith.science/pith/JROGOWEXMOOOL74QGCBVBEKTFO/action/author_attestation","sign_citation":"https://pith.science/pith/JROGOWEXMOOOL74QGCBVBEKTFO/action/citation_signature","submit_replication":"https://pith.science/pith/JROGOWEXMOOOL74QGCBVBEKTFO/action/replication_record"}},"created_at":"2026-05-18T01:25:09.081523+00:00","updated_at":"2026-05-18T01:25:09.081523+00:00"}