{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:JGRZEHP7ZT66LAZKQY4GNWXAXC","short_pith_number":"pith:JGRZEHP7","schema_version":"1.0","canonical_sha256":"49a3921dffccfde5832a863866dae0b8b2717e927f417f9a6fd39d389fed478f","source":{"kind":"arxiv","id":"1711.08710","version":1},"attestation_state":"computed","paper":{"title":"Vertex partitions of $(C_3,C_4,C_6)$-free planar graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Fran\\c{c}ois Dross, Pascal Ochem","submitted_at":"2017-11-23T14:36:15Z","abstract_excerpt":"A graph is $(k_1,k_2)$-colorable if its vertex set can be partitioned into a graph with maximum degree at most $k_1$ and and a graph with maximum degree at most $k_2$. We show that every $(C_3,C_4,C_6)$-free planar graph is $(0,6)$-colorable. We also show that deciding whether a $(C_3,C_4,C_6)$-free planar graph is $(0,3)$-colorable is NP-complete."},"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":"1711.08710","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-11-23T14:36:15Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"ebeb66ff1e9888b5d34d95a4eab7e041e3d1cf64ba22cec4ca6c0c84ba600c12","abstract_canon_sha256":"b34f5ec2059c6aea95ff6e9f1ede149c54ba628dd4661c03f92d528f4dba3ce7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:44.338927Z","signature_b64":"YOU/nh1le2eZWCtiu13BYAIMQG9d8o2mfzBp0r9FIZ4ZLQFP8BORDipzl1+0g05hpuSx/G7/4OyaR2eyQJCtBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"49a3921dffccfde5832a863866dae0b8b2717e927f417f9a6fd39d389fed478f","last_reissued_at":"2026-05-18T00:29:44.338423Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:44.338423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Vertex partitions of $(C_3,C_4,C_6)$-free planar graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Fran\\c{c}ois Dross, Pascal Ochem","submitted_at":"2017-11-23T14:36:15Z","abstract_excerpt":"A graph is $(k_1,k_2)$-colorable if its vertex set can be partitioned into a graph with maximum degree at most $k_1$ and and a graph with maximum degree at most $k_2$. We show that every $(C_3,C_4,C_6)$-free planar graph is $(0,6)$-colorable. We also show that deciding whether a $(C_3,C_4,C_6)$-free planar graph is $(0,3)$-colorable is NP-complete."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.08710","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":"1711.08710","created_at":"2026-05-18T00:29:44.338498+00:00"},{"alias_kind":"arxiv_version","alias_value":"1711.08710v1","created_at":"2026-05-18T00:29:44.338498+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.08710","created_at":"2026-05-18T00:29:44.338498+00:00"},{"alias_kind":"pith_short_12","alias_value":"JGRZEHP7ZT66","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_16","alias_value":"JGRZEHP7ZT66LAZK","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_8","alias_value":"JGRZEHP7","created_at":"2026-05-18T12:31:24.725408+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/JGRZEHP7ZT66LAZKQY4GNWXAXC","json":"https://pith.science/pith/JGRZEHP7ZT66LAZKQY4GNWXAXC.json","graph_json":"https://pith.science/api/pith-number/JGRZEHP7ZT66LAZKQY4GNWXAXC/graph.json","events_json":"https://pith.science/api/pith-number/JGRZEHP7ZT66LAZKQY4GNWXAXC/events.json","paper":"https://pith.science/paper/JGRZEHP7"},"agent_actions":{"view_html":"https://pith.science/pith/JGRZEHP7ZT66LAZKQY4GNWXAXC","download_json":"https://pith.science/pith/JGRZEHP7ZT66LAZKQY4GNWXAXC.json","view_paper":"https://pith.science/paper/JGRZEHP7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1711.08710&json=true","fetch_graph":"https://pith.science/api/pith-number/JGRZEHP7ZT66LAZKQY4GNWXAXC/graph.json","fetch_events":"https://pith.science/api/pith-number/JGRZEHP7ZT66LAZKQY4GNWXAXC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JGRZEHP7ZT66LAZKQY4GNWXAXC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JGRZEHP7ZT66LAZKQY4GNWXAXC/action/storage_attestation","attest_author":"https://pith.science/pith/JGRZEHP7ZT66LAZKQY4GNWXAXC/action/author_attestation","sign_citation":"https://pith.science/pith/JGRZEHP7ZT66LAZKQY4GNWXAXC/action/citation_signature","submit_replication":"https://pith.science/pith/JGRZEHP7ZT66LAZKQY4GNWXAXC/action/replication_record"}},"created_at":"2026-05-18T00:29:44.338498+00:00","updated_at":"2026-05-18T00:29:44.338498+00:00"}