{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:VE4TPETQZDIGAMZEUBA47FJOLX","short_pith_number":"pith:VE4TPETQ","schema_version":"1.0","canonical_sha256":"a939379270c8d0603324a041cf952e5dcde2192cf47c73cab2bf8023c6ee6999","source":{"kind":"arxiv","id":"1710.10455","version":1},"attestation_state":"computed","paper":{"title":"All partitions have small parts - Gallai-Ramsey numbers of bipartite graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Colton Magnant, Haibo Wu, Pouria Salehi Nowbandegani, Suman Xia","submitted_at":"2017-10-28T12:08:50Z","abstract_excerpt":"Gallai-colorings are edge-colored complete graphs in which there are no rainbow triangles. Within such colored complete graphs, we consider Ramsey-type questions, looking for specified monochromatic graphs. In this work, we consider monochromatic bipartite graphs since the numbers are known to grow more slowly than for non-bipartite graphs. The main result shows that it suffices to consider only $3$-colorings which have a special partition of the vertices. Using this tool, we find several sharp numbers and conjecture the sharp value for all bipartite graphs. In particular, we determine the Gal"},"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":"1710.10455","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-28T12:08:50Z","cross_cats_sorted":[],"title_canon_sha256":"70b2a3b33c063562864a14ca2a92b428f80745166abbfc7dde6243034151ff2f","abstract_canon_sha256":"747ae021ad4be1836652b2e7817d81fefdf2ec7a4d9b8eea2abb00ade4e55f06"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:49.455132Z","signature_b64":"vYw1HgVj5uW/ubfm1Uj4jXE7w6XjqXCE5OWodfzPO7MmUg8rS2nsQKuEvJPb6MJbVKiB7hX5ERleCR8qUQY7Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a939379270c8d0603324a041cf952e5dcde2192cf47c73cab2bf8023c6ee6999","last_reissued_at":"2026-05-18T00:31:49.454606Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:49.454606Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"All partitions have small parts - Gallai-Ramsey numbers of bipartite graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Colton Magnant, Haibo Wu, Pouria Salehi Nowbandegani, Suman Xia","submitted_at":"2017-10-28T12:08:50Z","abstract_excerpt":"Gallai-colorings are edge-colored complete graphs in which there are no rainbow triangles. Within such colored complete graphs, we consider Ramsey-type questions, looking for specified monochromatic graphs. In this work, we consider monochromatic bipartite graphs since the numbers are known to grow more slowly than for non-bipartite graphs. The main result shows that it suffices to consider only $3$-colorings which have a special partition of the vertices. Using this tool, we find several sharp numbers and conjecture the sharp value for all bipartite graphs. In particular, we determine the Gal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10455","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":"1710.10455","created_at":"2026-05-18T00:31:49.454694+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.10455v1","created_at":"2026-05-18T00:31:49.454694+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.10455","created_at":"2026-05-18T00:31:49.454694+00:00"},{"alias_kind":"pith_short_12","alias_value":"VE4TPETQZDIG","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_16","alias_value":"VE4TPETQZDIGAMZE","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_8","alias_value":"VE4TPETQ","created_at":"2026-05-18T12:31:49.984773+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/VE4TPETQZDIGAMZEUBA47FJOLX","json":"https://pith.science/pith/VE4TPETQZDIGAMZEUBA47FJOLX.json","graph_json":"https://pith.science/api/pith-number/VE4TPETQZDIGAMZEUBA47FJOLX/graph.json","events_json":"https://pith.science/api/pith-number/VE4TPETQZDIGAMZEUBA47FJOLX/events.json","paper":"https://pith.science/paper/VE4TPETQ"},"agent_actions":{"view_html":"https://pith.science/pith/VE4TPETQZDIGAMZEUBA47FJOLX","download_json":"https://pith.science/pith/VE4TPETQZDIGAMZEUBA47FJOLX.json","view_paper":"https://pith.science/paper/VE4TPETQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.10455&json=true","fetch_graph":"https://pith.science/api/pith-number/VE4TPETQZDIGAMZEUBA47FJOLX/graph.json","fetch_events":"https://pith.science/api/pith-number/VE4TPETQZDIGAMZEUBA47FJOLX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VE4TPETQZDIGAMZEUBA47FJOLX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VE4TPETQZDIGAMZEUBA47FJOLX/action/storage_attestation","attest_author":"https://pith.science/pith/VE4TPETQZDIGAMZEUBA47FJOLX/action/author_attestation","sign_citation":"https://pith.science/pith/VE4TPETQZDIGAMZEUBA47FJOLX/action/citation_signature","submit_replication":"https://pith.science/pith/VE4TPETQZDIGAMZEUBA47FJOLX/action/replication_record"}},"created_at":"2026-05-18T00:31:49.454694+00:00","updated_at":"2026-05-18T00:31:49.454694+00:00"}