{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:4DMJVJGE5P3VZU5LFJLC2GFJSS","short_pith_number":"pith:4DMJVJGE","schema_version":"1.0","canonical_sha256":"e0d89aa4c4ebf75cd3ab2a562d18a99482209959b5216657cb29944d8c1c49d9","source":{"kind":"arxiv","id":"1407.0043","version":1},"attestation_state":"computed","paper":{"title":"Edge-colorings of $K_{m,n}$ which Forbid Multicolored Cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hung-Lin Fu, Ryo-Yu Pei, Yuan-Hsun Lo","submitted_at":"2014-06-30T20:17:24Z","abstract_excerpt":"A subgraph in an edge-colored graph is multicolored if all its edges receive distinct colors. In this paper, we study the proper edge-colorings of the complete bipartite graph $K_{m,n}$ which forbid multicolored cycles. Mainly, we prove that (1) for any integer $k\\geq 2$, if $n\\geq 5k-6$, then any properly $n$-edge-colored $K_{k,n}$ contains a multicolored $C_{2k}$, and (2) determine the order of the properly edge-colored complete bipartite graphs which forbid multicolored $C_6$."},"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":"1407.0043","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-30T20:17:24Z","cross_cats_sorted":[],"title_canon_sha256":"39a4b524b87a4363f020f64bbf9f2701bd9e961ed044153bb77df93dfeac04d8","abstract_canon_sha256":"bfa442c18e49d47f4d5d8138c4d0dac6228339c19ebd466ad057c31947e19fea"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:35.403933Z","signature_b64":"Oy7KeM57nCZNhCvgBJvw7ZXSioBn0xFViZjrxGVjnma/G4goCdU1W+2leu+tKCcUqbAoSnUZWB58VJR18sSlCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e0d89aa4c4ebf75cd3ab2a562d18a99482209959b5216657cb29944d8c1c49d9","last_reissued_at":"2026-05-18T02:48:35.403301Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:35.403301Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Edge-colorings of $K_{m,n}$ which Forbid Multicolored Cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hung-Lin Fu, Ryo-Yu Pei, Yuan-Hsun Lo","submitted_at":"2014-06-30T20:17:24Z","abstract_excerpt":"A subgraph in an edge-colored graph is multicolored if all its edges receive distinct colors. In this paper, we study the proper edge-colorings of the complete bipartite graph $K_{m,n}$ which forbid multicolored cycles. Mainly, we prove that (1) for any integer $k\\geq 2$, if $n\\geq 5k-6$, then any properly $n$-edge-colored $K_{k,n}$ contains a multicolored $C_{2k}$, and (2) determine the order of the properly edge-colored complete bipartite graphs which forbid multicolored $C_6$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0043","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":"1407.0043","created_at":"2026-05-18T02:48:35.403408+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.0043v1","created_at":"2026-05-18T02:48:35.403408+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.0043","created_at":"2026-05-18T02:48:35.403408+00:00"},{"alias_kind":"pith_short_12","alias_value":"4DMJVJGE5P3V","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_16","alias_value":"4DMJVJGE5P3VZU5L","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_8","alias_value":"4DMJVJGE","created_at":"2026-05-18T12:28:14.216126+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/4DMJVJGE5P3VZU5LFJLC2GFJSS","json":"https://pith.science/pith/4DMJVJGE5P3VZU5LFJLC2GFJSS.json","graph_json":"https://pith.science/api/pith-number/4DMJVJGE5P3VZU5LFJLC2GFJSS/graph.json","events_json":"https://pith.science/api/pith-number/4DMJVJGE5P3VZU5LFJLC2GFJSS/events.json","paper":"https://pith.science/paper/4DMJVJGE"},"agent_actions":{"view_html":"https://pith.science/pith/4DMJVJGE5P3VZU5LFJLC2GFJSS","download_json":"https://pith.science/pith/4DMJVJGE5P3VZU5LFJLC2GFJSS.json","view_paper":"https://pith.science/paper/4DMJVJGE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.0043&json=true","fetch_graph":"https://pith.science/api/pith-number/4DMJVJGE5P3VZU5LFJLC2GFJSS/graph.json","fetch_events":"https://pith.science/api/pith-number/4DMJVJGE5P3VZU5LFJLC2GFJSS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4DMJVJGE5P3VZU5LFJLC2GFJSS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4DMJVJGE5P3VZU5LFJLC2GFJSS/action/storage_attestation","attest_author":"https://pith.science/pith/4DMJVJGE5P3VZU5LFJLC2GFJSS/action/author_attestation","sign_citation":"https://pith.science/pith/4DMJVJGE5P3VZU5LFJLC2GFJSS/action/citation_signature","submit_replication":"https://pith.science/pith/4DMJVJGE5P3VZU5LFJLC2GFJSS/action/replication_record"}},"created_at":"2026-05-18T02:48:35.403408+00:00","updated_at":"2026-05-18T02:48:35.403408+00:00"}