{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:ULRJWLC6CM3WI2JBI33SV3455P","short_pith_number":"pith:ULRJWLC6","schema_version":"1.0","canonical_sha256":"a2e29b2c5e133764692146f72aef9debd95e2c1fb9e8ed74857eda7d8b966f05","source":{"kind":"arxiv","id":"1508.01263","version":4},"attestation_state":"computed","paper":{"title":"Interval minors of complete multipartite graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hongjian Lai, Yaping Mao, Zhao Wang, Zhiwei Guo","submitted_at":"2015-08-06T02:19:36Z","abstract_excerpt":"Interval minors of bipartite graphs were introduced by Jacob Fox in the study of Stanley-Wilf limits. Recently, Mohar, Rafiey, Tayfeh-Rezaie and Wu investigated the maximum number of edges in $K_{k,\\ell}$-interval minor free bipartite graphs when $k=2$ and $k=3$. In this paper, we investigate the maximum number of edges in $K_{k,\\ell}$-interval minor free bipartite graphs for general $k$ and $\\ell$. We also study the maximum number of edges in $K_{\\ell_1,\\ell_2,\\cdots,\\ell_t}$-interval minor free multipartite graphs."},"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":"1508.01263","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-06T02:19:36Z","cross_cats_sorted":[],"title_canon_sha256":"6cd1be01537fc202c464692aed8ff09056192951542c426ecbcce378394df5c1","abstract_canon_sha256":"f70ff6687e952a44568d8090b515464481d7a932733152eb5a4e663775ca4c2e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:51.292680Z","signature_b64":"EmUeAJ5CsstjoCrbL83rZ0WhyTiu/gUO+Ga8LXPoaMLdb5I5actaijGZUJCP7TjvnS1Hqz4WvlkCEDwd+IgRDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2e29b2c5e133764692146f72aef9debd95e2c1fb9e8ed74857eda7d8b966f05","last_reissued_at":"2026-05-18T01:33:51.292001Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:51.292001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Interval minors of complete multipartite graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hongjian Lai, Yaping Mao, Zhao Wang, Zhiwei Guo","submitted_at":"2015-08-06T02:19:36Z","abstract_excerpt":"Interval minors of bipartite graphs were introduced by Jacob Fox in the study of Stanley-Wilf limits. Recently, Mohar, Rafiey, Tayfeh-Rezaie and Wu investigated the maximum number of edges in $K_{k,\\ell}$-interval minor free bipartite graphs when $k=2$ and $k=3$. In this paper, we investigate the maximum number of edges in $K_{k,\\ell}$-interval minor free bipartite graphs for general $k$ and $\\ell$. We also study the maximum number of edges in $K_{\\ell_1,\\ell_2,\\cdots,\\ell_t}$-interval minor free multipartite graphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01263","kind":"arxiv","version":4},"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":"1508.01263","created_at":"2026-05-18T01:33:51.292097+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.01263v4","created_at":"2026-05-18T01:33:51.292097+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.01263","created_at":"2026-05-18T01:33:51.292097+00:00"},{"alias_kind":"pith_short_12","alias_value":"ULRJWLC6CM3W","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_16","alias_value":"ULRJWLC6CM3WI2JB","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_8","alias_value":"ULRJWLC6","created_at":"2026-05-18T12:29:44.643036+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/ULRJWLC6CM3WI2JBI33SV3455P","json":"https://pith.science/pith/ULRJWLC6CM3WI2JBI33SV3455P.json","graph_json":"https://pith.science/api/pith-number/ULRJWLC6CM3WI2JBI33SV3455P/graph.json","events_json":"https://pith.science/api/pith-number/ULRJWLC6CM3WI2JBI33SV3455P/events.json","paper":"https://pith.science/paper/ULRJWLC6"},"agent_actions":{"view_html":"https://pith.science/pith/ULRJWLC6CM3WI2JBI33SV3455P","download_json":"https://pith.science/pith/ULRJWLC6CM3WI2JBI33SV3455P.json","view_paper":"https://pith.science/paper/ULRJWLC6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.01263&json=true","fetch_graph":"https://pith.science/api/pith-number/ULRJWLC6CM3WI2JBI33SV3455P/graph.json","fetch_events":"https://pith.science/api/pith-number/ULRJWLC6CM3WI2JBI33SV3455P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ULRJWLC6CM3WI2JBI33SV3455P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ULRJWLC6CM3WI2JBI33SV3455P/action/storage_attestation","attest_author":"https://pith.science/pith/ULRJWLC6CM3WI2JBI33SV3455P/action/author_attestation","sign_citation":"https://pith.science/pith/ULRJWLC6CM3WI2JBI33SV3455P/action/citation_signature","submit_replication":"https://pith.science/pith/ULRJWLC6CM3WI2JBI33SV3455P/action/replication_record"}},"created_at":"2026-05-18T01:33:51.292097+00:00","updated_at":"2026-05-18T01:33:51.292097+00:00"}