{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:R7SA3AUZMHZUEBMGWSVPGUSKBS","short_pith_number":"pith:R7SA3AUZ","schema_version":"1.0","canonical_sha256":"8fe40d829961f3420586b4aaf3524a0c83c408dfb3342a780c52d4c40d9f7184","source":{"kind":"arxiv","id":"1503.06595","version":2},"attestation_state":"computed","paper":{"title":"New bounds for the max-$k$-cut and chromatic number of a graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.OC","authors_text":"Edwin R. van Dam, Renata Sotirov","submitted_at":"2015-03-23T10:55:02Z","abstract_excerpt":"We consider several semidefinite programming relaxations for the max-$k$-cut problem, with increasing complexity. The optimal solution of the weakest presented semidefinite programming relaxation has a closed form expression that includes the largest Laplacian eigenvalue of the graph under consideration. This is the first known eigenvalue bound for the max-$k$-cut when $k>2$ that is applicable to any graph. This bound is exploited to derive a new eigenvalue bound on the chromatic number of a graph. For regular graphs, the new bound on the chromatic number is the same as the well-known Hoffman "},"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":"1503.06595","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-03-23T10:55:02Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"8f697df8127e434d28f1fc035f1f05f98b8d0f64a525aeb88a981994d57277e7","abstract_canon_sha256":"7ba081bb8e3b80a6e7ea3a9d751ca47249c92981f3c7c28d8b632a1fe7087e5b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:57.855842Z","signature_b64":"OCPb511weKBTCIG4JP9UWirKZyoCNzhNruV6EbQxKqhjC/rBKYV8ENJ53Lh5iAQsJoDFogLBmrN674Pc+/nZAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8fe40d829961f3420586b4aaf3524a0c83c408dfb3342a780c52d4c40d9f7184","last_reissued_at":"2026-05-18T01:26:57.855124Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:57.855124Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"New bounds for the max-$k$-cut and chromatic number of a graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.OC","authors_text":"Edwin R. van Dam, Renata Sotirov","submitted_at":"2015-03-23T10:55:02Z","abstract_excerpt":"We consider several semidefinite programming relaxations for the max-$k$-cut problem, with increasing complexity. The optimal solution of the weakest presented semidefinite programming relaxation has a closed form expression that includes the largest Laplacian eigenvalue of the graph under consideration. This is the first known eigenvalue bound for the max-$k$-cut when $k>2$ that is applicable to any graph. This bound is exploited to derive a new eigenvalue bound on the chromatic number of a graph. For regular graphs, the new bound on the chromatic number is the same as the well-known Hoffman "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06595","kind":"arxiv","version":2},"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":"1503.06595","created_at":"2026-05-18T01:26:57.855249+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.06595v2","created_at":"2026-05-18T01:26:57.855249+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.06595","created_at":"2026-05-18T01:26:57.855249+00:00"},{"alias_kind":"pith_short_12","alias_value":"R7SA3AUZMHZU","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_16","alias_value":"R7SA3AUZMHZUEBMG","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_8","alias_value":"R7SA3AUZ","created_at":"2026-05-18T12:29:39.896362+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/R7SA3AUZMHZUEBMGWSVPGUSKBS","json":"https://pith.science/pith/R7SA3AUZMHZUEBMGWSVPGUSKBS.json","graph_json":"https://pith.science/api/pith-number/R7SA3AUZMHZUEBMGWSVPGUSKBS/graph.json","events_json":"https://pith.science/api/pith-number/R7SA3AUZMHZUEBMGWSVPGUSKBS/events.json","paper":"https://pith.science/paper/R7SA3AUZ"},"agent_actions":{"view_html":"https://pith.science/pith/R7SA3AUZMHZUEBMGWSVPGUSKBS","download_json":"https://pith.science/pith/R7SA3AUZMHZUEBMGWSVPGUSKBS.json","view_paper":"https://pith.science/paper/R7SA3AUZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.06595&json=true","fetch_graph":"https://pith.science/api/pith-number/R7SA3AUZMHZUEBMGWSVPGUSKBS/graph.json","fetch_events":"https://pith.science/api/pith-number/R7SA3AUZMHZUEBMGWSVPGUSKBS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/R7SA3AUZMHZUEBMGWSVPGUSKBS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/R7SA3AUZMHZUEBMGWSVPGUSKBS/action/storage_attestation","attest_author":"https://pith.science/pith/R7SA3AUZMHZUEBMGWSVPGUSKBS/action/author_attestation","sign_citation":"https://pith.science/pith/R7SA3AUZMHZUEBMGWSVPGUSKBS/action/citation_signature","submit_replication":"https://pith.science/pith/R7SA3AUZMHZUEBMGWSVPGUSKBS/action/replication_record"}},"created_at":"2026-05-18T01:26:57.855249+00:00","updated_at":"2026-05-18T01:26:57.855249+00:00"}