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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 ","authors_text":"Hong Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-07-26T16:33:57Z","title":"Partition of a Subset into Two Directed Cycles with Partial Degrees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.11668","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:135775e80c524f1cd5cf172747a6176dc212593c2e50a5a23641ccdfac09e460","target":"record","created_at":"2026-05-17T23:39:28Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"f2330d7ea9b734ca32b4f9510252b13f9eb91676a2c8882ce55ec0b18e3b721e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-07-26T16:33:57Z","title_canon_sha256":"87debe9023af079f0f25b7f176a8f568c447030ffeeb5f0d3149c54eec517423"},"schema_version":"1.0","source":{"id":"1907.11668","kind":"arxiv","version":1}},"canonical_sha256":"0049d468f7727dbdbdff0fff8864ab3bb1bcae06ad95b3a220f6311863a5cb3e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0049d468f7727dbdbdff0fff8864ab3bb1bcae06ad95b3a220f6311863a5cb3e","first_computed_at":"2026-05-17T23:39:28.308088Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:28.308088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lg7Ou6tlOTVMIhzDi6E8N45w92kefPS+6KyG0UAb5+LFTbWhfNhySjhfdZ7YMIpLLxOK5voHSUjI+/zcBpRrAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:28.309226Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.11668","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:135775e80c524f1cd5cf172747a6176dc212593c2e50a5a23641ccdfac09e460","sha256:c8be3be904bcfee41a5a08a4a7905ee249d8ee74298af54c536e66e70e0040f4"],"state_sha256":"b2def8e07316941c817f4ceed3f8f65021bdbcbebbd77cf26721f6f3d26565a3"}