{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:DX5LYLC7T6NYGSJFYZBUL5ZLF3","short_pith_number":"pith:DX5LYLC7","schema_version":"1.0","canonical_sha256":"1dfabc2c5f9f9b834925c64345f72b2ed8ba96fac9ff6ec404136c37b87dcd9e","source":{"kind":"arxiv","id":"1504.01975","version":1},"attestation_state":"computed","paper":{"title":"On the b-chromatic number of the Cartesian product of two complete graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Artur Mesquita Barbosa, Fr\\'ed\\'eric Maffray","submitted_at":"2015-04-08T14:09:19Z","abstract_excerpt":"A b-coloring of a graph $G$ is a coloring of its vertices such that every color class contains a vertex that has neighbors in all other classes. The b-chromatic number of $G$ is the largest integer $k$ such that $G$ has a b-coloring with $k$ colors. Javadi and Omoomi (\"On b-coloring of cartesian product of graphs\", Ars Combinatoria 107 (2012) 521-536) proved that the b-chromatic number of $K_n \\times K_n$ (the Cartesian product of two complete graphs on $n$ vertices) is in the set $\\{2n-3, 2n-2\\}$ and conjectured that the exact value is $2n-3$ for all $n \\ge 5$. We give counterexamples to this"},"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":"1504.01975","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-04-08T14:09:19Z","cross_cats_sorted":[],"title_canon_sha256":"ea9ccf92ab212b8ca7096aab0125a6bea71048327494b30ff01b627a731fb019","abstract_canon_sha256":"87fb76a058c36474ad636d3dbe2bc3b96d40d4efffdd014bcd008636662f9d89"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:19:17.635059Z","signature_b64":"ZU6X9wDgDeIkCzcl+6DMns+8MtxjOz9xzlNXItywBM0JGiA0WiNgfL6k+Q7da/tm60mWNTsrEwUw3UVhYYDXAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1dfabc2c5f9f9b834925c64345f72b2ed8ba96fac9ff6ec404136c37b87dcd9e","last_reissued_at":"2026-05-18T02:19:17.634559Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:19:17.634559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the b-chromatic number of the Cartesian product of two complete graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Artur Mesquita Barbosa, Fr\\'ed\\'eric Maffray","submitted_at":"2015-04-08T14:09:19Z","abstract_excerpt":"A b-coloring of a graph $G$ is a coloring of its vertices such that every color class contains a vertex that has neighbors in all other classes. The b-chromatic number of $G$ is the largest integer $k$ such that $G$ has a b-coloring with $k$ colors. Javadi and Omoomi (\"On b-coloring of cartesian product of graphs\", Ars Combinatoria 107 (2012) 521-536) proved that the b-chromatic number of $K_n \\times K_n$ (the Cartesian product of two complete graphs on $n$ vertices) is in the set $\\{2n-3, 2n-2\\}$ and conjectured that the exact value is $2n-3$ for all $n \\ge 5$. We give counterexamples to this"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01975","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":"1504.01975","created_at":"2026-05-18T02:19:17.634629+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.01975v1","created_at":"2026-05-18T02:19:17.634629+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.01975","created_at":"2026-05-18T02:19:17.634629+00:00"},{"alias_kind":"pith_short_12","alias_value":"DX5LYLC7T6NY","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_16","alias_value":"DX5LYLC7T6NYGSJF","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_8","alias_value":"DX5LYLC7","created_at":"2026-05-18T12:29:17.054201+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/DX5LYLC7T6NYGSJFYZBUL5ZLF3","json":"https://pith.science/pith/DX5LYLC7T6NYGSJFYZBUL5ZLF3.json","graph_json":"https://pith.science/api/pith-number/DX5LYLC7T6NYGSJFYZBUL5ZLF3/graph.json","events_json":"https://pith.science/api/pith-number/DX5LYLC7T6NYGSJFYZBUL5ZLF3/events.json","paper":"https://pith.science/paper/DX5LYLC7"},"agent_actions":{"view_html":"https://pith.science/pith/DX5LYLC7T6NYGSJFYZBUL5ZLF3","download_json":"https://pith.science/pith/DX5LYLC7T6NYGSJFYZBUL5ZLF3.json","view_paper":"https://pith.science/paper/DX5LYLC7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.01975&json=true","fetch_graph":"https://pith.science/api/pith-number/DX5LYLC7T6NYGSJFYZBUL5ZLF3/graph.json","fetch_events":"https://pith.science/api/pith-number/DX5LYLC7T6NYGSJFYZBUL5ZLF3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DX5LYLC7T6NYGSJFYZBUL5ZLF3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DX5LYLC7T6NYGSJFYZBUL5ZLF3/action/storage_attestation","attest_author":"https://pith.science/pith/DX5LYLC7T6NYGSJFYZBUL5ZLF3/action/author_attestation","sign_citation":"https://pith.science/pith/DX5LYLC7T6NYGSJFYZBUL5ZLF3/action/citation_signature","submit_replication":"https://pith.science/pith/DX5LYLC7T6NYGSJFYZBUL5ZLF3/action/replication_record"}},"created_at":"2026-05-18T02:19:17.634629+00:00","updated_at":"2026-05-18T02:19:17.634629+00:00"}