{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:KNFDWWQMT2TATPORVGS2Y4R5FU","short_pith_number":"pith:KNFDWWQM","schema_version":"1.0","canonical_sha256":"534a3b5a0c9ea609bdd1a9a5ac723d2d2ebf6ff3c7e11331376bf8a31a6dbf47","source":{"kind":"arxiv","id":"1607.06393","version":2},"attestation_state":"computed","paper":{"title":"On two problems in Ramsey-Tur\\'an theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hong Liu, J\\'ozsef Balogh, Maryam Sharifzadeh","submitted_at":"2016-07-21T17:02:08Z","abstract_excerpt":"Alon, Balogh, Keevash and Sudakov proved that the $(k-1)$-partite Tur\\'an graph maximizes the number of distinct $r$-edge-colorings with no monochromatic $K_k$ for all fixed $k$ and $r=2,3$, among all $n$-vertex graphs. In this paper, we determine this function asymptotically for $r=2$ among $n$-vertex graphs with sub-linear independence number. Somewhat surprisingly, unlike Alon-Balogh-Keevash-Sudakov's result, the extremal construction from Ramsey-Tur\\'an theory, as a natural candidate, does not maximize the number of distinct edge-colorings with no monochromatic cliques among all graphs wit"},"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":"1607.06393","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-07-21T17:02:08Z","cross_cats_sorted":[],"title_canon_sha256":"d6316ee268a2fa6e9e4db3d56cbd1c4e6e22436435bcab948151bc9065b6f2df","abstract_canon_sha256":"0a8382f183ca7f9419231c797f626b61e21f87481b66a3fda7c7d98904e90b84"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:54.351211Z","signature_b64":"T4AtWaLn+OtXb2bHJHbTaCF/+Gekpnmcy0RCI4sNmIytxxxLhpfoh+H9n2F3x3b9pVlL18vYnMi/F+wvNCzqDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"534a3b5a0c9ea609bdd1a9a5ac723d2d2ebf6ff3c7e11331376bf8a31a6dbf47","last_reissued_at":"2026-05-18T00:45:54.350509Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:54.350509Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On two problems in Ramsey-Tur\\'an theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hong Liu, J\\'ozsef Balogh, Maryam Sharifzadeh","submitted_at":"2016-07-21T17:02:08Z","abstract_excerpt":"Alon, Balogh, Keevash and Sudakov proved that the $(k-1)$-partite Tur\\'an graph maximizes the number of distinct $r$-edge-colorings with no monochromatic $K_k$ for all fixed $k$ and $r=2,3$, among all $n$-vertex graphs. In this paper, we determine this function asymptotically for $r=2$ among $n$-vertex graphs with sub-linear independence number. Somewhat surprisingly, unlike Alon-Balogh-Keevash-Sudakov's result, the extremal construction from Ramsey-Tur\\'an theory, as a natural candidate, does not maximize the number of distinct edge-colorings with no monochromatic cliques among all graphs wit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.06393","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":"1607.06393","created_at":"2026-05-18T00:45:54.350615+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.06393v2","created_at":"2026-05-18T00:45:54.350615+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.06393","created_at":"2026-05-18T00:45:54.350615+00:00"},{"alias_kind":"pith_short_12","alias_value":"KNFDWWQMT2TA","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_16","alias_value":"KNFDWWQMT2TATPOR","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_8","alias_value":"KNFDWWQM","created_at":"2026-05-18T12:30:25.849896+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/KNFDWWQMT2TATPORVGS2Y4R5FU","json":"https://pith.science/pith/KNFDWWQMT2TATPORVGS2Y4R5FU.json","graph_json":"https://pith.science/api/pith-number/KNFDWWQMT2TATPORVGS2Y4R5FU/graph.json","events_json":"https://pith.science/api/pith-number/KNFDWWQMT2TATPORVGS2Y4R5FU/events.json","paper":"https://pith.science/paper/KNFDWWQM"},"agent_actions":{"view_html":"https://pith.science/pith/KNFDWWQMT2TATPORVGS2Y4R5FU","download_json":"https://pith.science/pith/KNFDWWQMT2TATPORVGS2Y4R5FU.json","view_paper":"https://pith.science/paper/KNFDWWQM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.06393&json=true","fetch_graph":"https://pith.science/api/pith-number/KNFDWWQMT2TATPORVGS2Y4R5FU/graph.json","fetch_events":"https://pith.science/api/pith-number/KNFDWWQMT2TATPORVGS2Y4R5FU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KNFDWWQMT2TATPORVGS2Y4R5FU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KNFDWWQMT2TATPORVGS2Y4R5FU/action/storage_attestation","attest_author":"https://pith.science/pith/KNFDWWQMT2TATPORVGS2Y4R5FU/action/author_attestation","sign_citation":"https://pith.science/pith/KNFDWWQMT2TATPORVGS2Y4R5FU/action/citation_signature","submit_replication":"https://pith.science/pith/KNFDWWQMT2TATPORVGS2Y4R5FU/action/replication_record"}},"created_at":"2026-05-18T00:45:54.350615+00:00","updated_at":"2026-05-18T00:45:54.350615+00:00"}