{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:BFEUCWOYR3GWC7DZDW67ZAWNSI","short_pith_number":"pith:BFEUCWOY","schema_version":"1.0","canonical_sha256":"09494159d88ecd617c791dbdfc82cd920b4a0151c7ca6d32ec8c97e4f4c15860","source":{"kind":"arxiv","id":"1905.12414","version":1},"attestation_state":"computed","paper":{"title":"Ramsey and Gallai-Ramsey number for wheels","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Colton Magnant, Ingo Schiermeyer, Yaping Mao, Zhao Wang","submitted_at":"2019-05-28T13:18:45Z","abstract_excerpt":"Given a graph $G$ and a positive integer $k$, define the \\emph{Gallai-Ramsey number} to be the minimum number of vertices $n$ such that any $k$-edge coloring of $K_n$ contains either a rainbow (all different colored) triangle or a monochromatic copy of $G$. Much like graph Ramsey numbers, Gallai-Ramsey numbers have gained a reputation as being very difficult to compute in general. As yet, still only precious few sharp results are known. In this paper, we obtain bounds on the Gallai-Ramsey number for wheels and the exact value for the wheel on $5$ vertices."},"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":"1905.12414","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2019-05-28T13:18:45Z","cross_cats_sorted":[],"title_canon_sha256":"002ce70b610e922e04eeacbef3521604ea1e4a13bb139cc3f7a685780f93eb47","abstract_canon_sha256":"6603a27b6ebc9fbac8543420edcf0bf42c87a13eac76d26d53f048ac9f1f63e1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:44.409503Z","signature_b64":"YFsDCTpBoLz32HjVGzFNi4aaKxahwdcZeS1TcwwPw6etgvkhyJFnIMyVBTl522tZbkSVhC3cvs7pSft3LSz0AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"09494159d88ecd617c791dbdfc82cd920b4a0151c7ca6d32ec8c97e4f4c15860","last_reissued_at":"2026-05-17T23:44:44.409054Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:44.409054Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ramsey and Gallai-Ramsey number for wheels","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Colton Magnant, Ingo Schiermeyer, Yaping Mao, Zhao Wang","submitted_at":"2019-05-28T13:18:45Z","abstract_excerpt":"Given a graph $G$ and a positive integer $k$, define the \\emph{Gallai-Ramsey number} to be the minimum number of vertices $n$ such that any $k$-edge coloring of $K_n$ contains either a rainbow (all different colored) triangle or a monochromatic copy of $G$. Much like graph Ramsey numbers, Gallai-Ramsey numbers have gained a reputation as being very difficult to compute in general. As yet, still only precious few sharp results are known. In this paper, we obtain bounds on the Gallai-Ramsey number for wheels and the exact value for the wheel on $5$ vertices."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.12414","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":"1905.12414","created_at":"2026-05-17T23:44:44.409119+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.12414v1","created_at":"2026-05-17T23:44:44.409119+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.12414","created_at":"2026-05-17T23:44:44.409119+00:00"},{"alias_kind":"pith_short_12","alias_value":"BFEUCWOYR3GW","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_16","alias_value":"BFEUCWOYR3GWC7DZ","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_8","alias_value":"BFEUCWOY","created_at":"2026-05-18T12:33:12.712433+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/BFEUCWOYR3GWC7DZDW67ZAWNSI","json":"https://pith.science/pith/BFEUCWOYR3GWC7DZDW67ZAWNSI.json","graph_json":"https://pith.science/api/pith-number/BFEUCWOYR3GWC7DZDW67ZAWNSI/graph.json","events_json":"https://pith.science/api/pith-number/BFEUCWOYR3GWC7DZDW67ZAWNSI/events.json","paper":"https://pith.science/paper/BFEUCWOY"},"agent_actions":{"view_html":"https://pith.science/pith/BFEUCWOYR3GWC7DZDW67ZAWNSI","download_json":"https://pith.science/pith/BFEUCWOYR3GWC7DZDW67ZAWNSI.json","view_paper":"https://pith.science/paper/BFEUCWOY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.12414&json=true","fetch_graph":"https://pith.science/api/pith-number/BFEUCWOYR3GWC7DZDW67ZAWNSI/graph.json","fetch_events":"https://pith.science/api/pith-number/BFEUCWOYR3GWC7DZDW67ZAWNSI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BFEUCWOYR3GWC7DZDW67ZAWNSI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BFEUCWOYR3GWC7DZDW67ZAWNSI/action/storage_attestation","attest_author":"https://pith.science/pith/BFEUCWOYR3GWC7DZDW67ZAWNSI/action/author_attestation","sign_citation":"https://pith.science/pith/BFEUCWOYR3GWC7DZDW67ZAWNSI/action/citation_signature","submit_replication":"https://pith.science/pith/BFEUCWOYR3GWC7DZDW67ZAWNSI/action/replication_record"}},"created_at":"2026-05-17T23:44:44.409119+00:00","updated_at":"2026-05-17T23:44:44.409119+00:00"}