{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:BBPPG43FPVRSP4K6KVMWPZIBF7","short_pith_number":"pith:BBPPG43F","schema_version":"1.0","canonical_sha256":"085ef373657d6327f15e555967e5012fcc300d36881bb0868e8d593bf3e465b0","source":{"kind":"arxiv","id":"1411.6226","version":1},"attestation_state":"computed","paper":{"title":"Disjoint paths in tournaments","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alex Scott, Maria Chudnovsky, Paul Seymour","submitted_at":"2014-11-23T11:17:38Z","abstract_excerpt":"Given $k$ pairs of vertices $(s_i,t_i)$, $1\\le i\\le k$, of a digraph $G$, how can we test whether there exist $k$ vertex-disjoint directed paths from $s_i$ to $t_i$ for $1\\le i\\le k$? This is NP-complete in general digraphs, even for $k = 2$, but for $k=2$ there is a polynomial-time algorithm when $G$ is a tournament (or more generally, a semicomplete digraph), due to Bang-Jensen and Thomassen. Here we prove that for all fixed $k$ there is a polynomial-time algorithm to solve the problem when $G$ is semicomplete."},"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":"1411.6226","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-11-23T11:17:38Z","cross_cats_sorted":[],"title_canon_sha256":"47c30f264cb7b45e4d1248552faa7b7d3a4933b958ac30dd866d50793da4227c","abstract_canon_sha256":"cb0e823b5b108290b86284aa2348e94a3aaed09230a4025edba35a4c85595e40"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:33:00.458083Z","signature_b64":"PTj3BsBdGuKodi2BDGGADViybIJwQEZr7AsHvOKfEufuPcK+ddrI443QOlSyQBOrbqMwesj9PmdqASIs0AZ5Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"085ef373657d6327f15e555967e5012fcc300d36881bb0868e8d593bf3e465b0","last_reissued_at":"2026-05-18T02:33:00.457754Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:33:00.457754Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Disjoint paths in tournaments","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alex Scott, Maria Chudnovsky, Paul Seymour","submitted_at":"2014-11-23T11:17:38Z","abstract_excerpt":"Given $k$ pairs of vertices $(s_i,t_i)$, $1\\le i\\le k$, of a digraph $G$, how can we test whether there exist $k$ vertex-disjoint directed paths from $s_i$ to $t_i$ for $1\\le i\\le k$? This is NP-complete in general digraphs, even for $k = 2$, but for $k=2$ there is a polynomial-time algorithm when $G$ is a tournament (or more generally, a semicomplete digraph), due to Bang-Jensen and Thomassen. Here we prove that for all fixed $k$ there is a polynomial-time algorithm to solve the problem when $G$ is semicomplete."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.6226","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":"1411.6226","created_at":"2026-05-18T02:33:00.457808+00:00"},{"alias_kind":"arxiv_version","alias_value":"1411.6226v1","created_at":"2026-05-18T02:33:00.457808+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.6226","created_at":"2026-05-18T02:33:00.457808+00:00"},{"alias_kind":"pith_short_12","alias_value":"BBPPG43FPVRS","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_16","alias_value":"BBPPG43FPVRSP4K6","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_8","alias_value":"BBPPG43F","created_at":"2026-05-18T12:28:22.404517+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/BBPPG43FPVRSP4K6KVMWPZIBF7","json":"https://pith.science/pith/BBPPG43FPVRSP4K6KVMWPZIBF7.json","graph_json":"https://pith.science/api/pith-number/BBPPG43FPVRSP4K6KVMWPZIBF7/graph.json","events_json":"https://pith.science/api/pith-number/BBPPG43FPVRSP4K6KVMWPZIBF7/events.json","paper":"https://pith.science/paper/BBPPG43F"},"agent_actions":{"view_html":"https://pith.science/pith/BBPPG43FPVRSP4K6KVMWPZIBF7","download_json":"https://pith.science/pith/BBPPG43FPVRSP4K6KVMWPZIBF7.json","view_paper":"https://pith.science/paper/BBPPG43F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1411.6226&json=true","fetch_graph":"https://pith.science/api/pith-number/BBPPG43FPVRSP4K6KVMWPZIBF7/graph.json","fetch_events":"https://pith.science/api/pith-number/BBPPG43FPVRSP4K6KVMWPZIBF7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BBPPG43FPVRSP4K6KVMWPZIBF7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BBPPG43FPVRSP4K6KVMWPZIBF7/action/storage_attestation","attest_author":"https://pith.science/pith/BBPPG43FPVRSP4K6KVMWPZIBF7/action/author_attestation","sign_citation":"https://pith.science/pith/BBPPG43FPVRSP4K6KVMWPZIBF7/action/citation_signature","submit_replication":"https://pith.science/pith/BBPPG43FPVRSP4K6KVMWPZIBF7/action/replication_record"}},"created_at":"2026-05-18T02:33:00.457808+00:00","updated_at":"2026-05-18T02:33:00.457808+00:00"}