{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:ABE5I2HXOJ633PP7B77YQZFLHO","short_pith_number":"pith:ABE5I2HX","schema_version":"1.0","canonical_sha256":"0049d468f7727dbdbdff0fff8864ab3bb1bcae06ad95b3a220f6311863a5cb3e","source":{"kind":"arxiv","id":"1907.11668","version":1},"attestation_state":"computed","paper":{"title":"Partition of a Subset into Two Directed Cycles with Partial Degrees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hong Wang","submitted_at":"2019-07-26T16:33:57Z","abstract_excerpt":"Let $D=(V,A)$ be a directed graph of order $n\\geq 6$. Let $W$ be a subset of $V$ with $|W|\\geq 6$. Suppose that every vertex of $W$ has degree at least $(3n-3)/2$ in $D$. Then for any integer partition $|W|=n_1+n_2$ with $n_1\\geq 3$ and $n_2\\geq 3$, $D$ contains two disjoint directed cycles $C_1$ and $C_2$ such that $|V(C_1)\\cap W|=n_1$ and $|V(C_2)\\cap W|=n_2$. We conjecture that for any integer partition $|W|=n_1+n_2+\\cdots +n_k$ with $k\\geq 3$ and $n_i\\geq 3(1\\leq i\\leq k)$, $D$ contains $k$ disjoint directed cycles $C_1,C_2,\\ldots , C_k$ such that $|V(C_i)\\cap W|=n_i$ for all $1\\leq i\\leq "},"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":"1907.11668","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-07-26T16:33:57Z","cross_cats_sorted":[],"title_canon_sha256":"87debe9023af079f0f25b7f176a8f568c447030ffeeb5f0d3149c54eec517423","abstract_canon_sha256":"f2330d7ea9b734ca32b4f9510252b13f9eb91676a2c8882ce55ec0b18e3b721e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:28.309226Z","signature_b64":"lg7Ou6tlOTVMIhzDi6E8N45w92kefPS+6KyG0UAb5+LFTbWhfNhySjhfdZ7YMIpLLxOK5voHSUjI+/zcBpRrAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0049d468f7727dbdbdff0fff8864ab3bb1bcae06ad95b3a220f6311863a5cb3e","last_reissued_at":"2026-05-17T23:39:28.308088Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:28.308088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Partition of a Subset into Two Directed Cycles with Partial Degrees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hong Wang","submitted_at":"2019-07-26T16:33:57Z","abstract_excerpt":"Let $D=(V,A)$ be a directed graph of order $n\\geq 6$. Let $W$ be a subset of $V$ with $|W|\\geq 6$. Suppose that every vertex of $W$ has degree at least $(3n-3)/2$ in $D$. Then for any integer partition $|W|=n_1+n_2$ with $n_1\\geq 3$ and $n_2\\geq 3$, $D$ contains two disjoint directed cycles $C_1$ and $C_2$ such that $|V(C_1)\\cap W|=n_1$ and $|V(C_2)\\cap W|=n_2$. We conjecture that for any integer partition $|W|=n_1+n_2+\\cdots +n_k$ with $k\\geq 3$ and $n_i\\geq 3(1\\leq i\\leq k)$, $D$ contains $k$ disjoint directed cycles $C_1,C_2,\\ldots , C_k$ such that $|V(C_i)\\cap W|=n_i$ for all $1\\leq i\\leq "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.11668","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":"1907.11668","created_at":"2026-05-17T23:39:28.308176+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.11668v1","created_at":"2026-05-17T23:39:28.308176+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.11668","created_at":"2026-05-17T23:39:28.308176+00:00"},{"alias_kind":"pith_short_12","alias_value":"ABE5I2HXOJ63","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_16","alias_value":"ABE5I2HXOJ633PP7","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_8","alias_value":"ABE5I2HX","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/ABE5I2HXOJ633PP7B77YQZFLHO","json":"https://pith.science/pith/ABE5I2HXOJ633PP7B77YQZFLHO.json","graph_json":"https://pith.science/api/pith-number/ABE5I2HXOJ633PP7B77YQZFLHO/graph.json","events_json":"https://pith.science/api/pith-number/ABE5I2HXOJ633PP7B77YQZFLHO/events.json","paper":"https://pith.science/paper/ABE5I2HX"},"agent_actions":{"view_html":"https://pith.science/pith/ABE5I2HXOJ633PP7B77YQZFLHO","download_json":"https://pith.science/pith/ABE5I2HXOJ633PP7B77YQZFLHO.json","view_paper":"https://pith.science/paper/ABE5I2HX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.11668&json=true","fetch_graph":"https://pith.science/api/pith-number/ABE5I2HXOJ633PP7B77YQZFLHO/graph.json","fetch_events":"https://pith.science/api/pith-number/ABE5I2HXOJ633PP7B77YQZFLHO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ABE5I2HXOJ633PP7B77YQZFLHO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ABE5I2HXOJ633PP7B77YQZFLHO/action/storage_attestation","attest_author":"https://pith.science/pith/ABE5I2HXOJ633PP7B77YQZFLHO/action/author_attestation","sign_citation":"https://pith.science/pith/ABE5I2HXOJ633PP7B77YQZFLHO/action/citation_signature","submit_replication":"https://pith.science/pith/ABE5I2HXOJ633PP7B77YQZFLHO/action/replication_record"}},"created_at":"2026-05-17T23:39:28.308176+00:00","updated_at":"2026-05-17T23:39:28.308176+00:00"}