{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:S3BFMVPHSP4POFST5T6KBTFAXH","short_pith_number":"pith:S3BFMVPH","schema_version":"1.0","canonical_sha256":"96c25655e793f8f71653ecfca0cca0b9e03dc12d642b8e0e882a6b3037e4185a","source":{"kind":"arxiv","id":"1807.08286","version":1},"attestation_state":"computed","paper":{"title":"On kernels by rainbow paths in arc-coloured digraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ruijuan Li, Yanqin Cao","submitted_at":"2018-07-22T14:01:07Z","abstract_excerpt":"In 2018, Bai, Fujita and Zhang (\\emph{Discrete Math.} 2018, 341(6): 1523-1533) introduced the concept of a kernel by rainbow paths (for short, RP-kernel) of an arc-coloured digraph $D$, which is a subset $S$ of vertices of $D$ such that ($a$) there exists no rainbow path for any pair of distinct vertices of $S$, and ($b$) every vertex outside $S$ can reach $S$ by a rainbow path in $D$. They showed that it is NP-hard to recognize wether an arc-coloured digraph has a RP-kernel and it is NP-complete to decided wether an arc-coloured tournament has a RP-kernel. In this paper, we give the sufficien"},"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":"1807.08286","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-22T14:01:07Z","cross_cats_sorted":[],"title_canon_sha256":"064236b34eeaedc9627a5f375e7a99d4020aee5a5287cca4e0319a04e3052da2","abstract_canon_sha256":"a271a026ebd9f2600bfc239ac40d9434008625e6e28adaca32eaa9203515a236"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:08.580469Z","signature_b64":"R64r3/+08fv4KSk4XLMt6yZpD39eII+2JtqYt8gBoqvnndQcC0BahPEekjTIF4eAV16AzKsCAzfvFTsrSsCtAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"96c25655e793f8f71653ecfca0cca0b9e03dc12d642b8e0e882a6b3037e4185a","last_reissued_at":"2026-05-18T00:10:08.579778Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:08.579778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On kernels by rainbow paths in arc-coloured digraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ruijuan Li, Yanqin Cao","submitted_at":"2018-07-22T14:01:07Z","abstract_excerpt":"In 2018, Bai, Fujita and Zhang (\\emph{Discrete Math.} 2018, 341(6): 1523-1533) introduced the concept of a kernel by rainbow paths (for short, RP-kernel) of an arc-coloured digraph $D$, which is a subset $S$ of vertices of $D$ such that ($a$) there exists no rainbow path for any pair of distinct vertices of $S$, and ($b$) every vertex outside $S$ can reach $S$ by a rainbow path in $D$. They showed that it is NP-hard to recognize wether an arc-coloured digraph has a RP-kernel and it is NP-complete to decided wether an arc-coloured tournament has a RP-kernel. In this paper, we give the sufficien"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.08286","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":"1807.08286","created_at":"2026-05-18T00:10:08.579896+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.08286v1","created_at":"2026-05-18T00:10:08.579896+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.08286","created_at":"2026-05-18T00:10:08.579896+00:00"},{"alias_kind":"pith_short_12","alias_value":"S3BFMVPHSP4P","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_16","alias_value":"S3BFMVPHSP4POFST","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_8","alias_value":"S3BFMVPH","created_at":"2026-05-18T12:32:50.500415+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/S3BFMVPHSP4POFST5T6KBTFAXH","json":"https://pith.science/pith/S3BFMVPHSP4POFST5T6KBTFAXH.json","graph_json":"https://pith.science/api/pith-number/S3BFMVPHSP4POFST5T6KBTFAXH/graph.json","events_json":"https://pith.science/api/pith-number/S3BFMVPHSP4POFST5T6KBTFAXH/events.json","paper":"https://pith.science/paper/S3BFMVPH"},"agent_actions":{"view_html":"https://pith.science/pith/S3BFMVPHSP4POFST5T6KBTFAXH","download_json":"https://pith.science/pith/S3BFMVPHSP4POFST5T6KBTFAXH.json","view_paper":"https://pith.science/paper/S3BFMVPH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.08286&json=true","fetch_graph":"https://pith.science/api/pith-number/S3BFMVPHSP4POFST5T6KBTFAXH/graph.json","fetch_events":"https://pith.science/api/pith-number/S3BFMVPHSP4POFST5T6KBTFAXH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S3BFMVPHSP4POFST5T6KBTFAXH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S3BFMVPHSP4POFST5T6KBTFAXH/action/storage_attestation","attest_author":"https://pith.science/pith/S3BFMVPHSP4POFST5T6KBTFAXH/action/author_attestation","sign_citation":"https://pith.science/pith/S3BFMVPHSP4POFST5T6KBTFAXH/action/citation_signature","submit_replication":"https://pith.science/pith/S3BFMVPHSP4POFST5T6KBTFAXH/action/replication_record"}},"created_at":"2026-05-18T00:10:08.579896+00:00","updated_at":"2026-05-18T00:10:08.579896+00:00"}