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Let $T$ be a digraph with $t$ vertices $u_1,\\dots , u_t$ and let $H_1,\\dots H_t$ be digraphs such that $H_i$ has vertices $u_{i,j_i},\\ 1\\le j_i\\le n_i.$ Then the composition $Q=T[H_1,\\dots , H_t]$ is a digraph with vertex set $\\{u_{i,j_i}\\mid 1\\le i\\le t, 1\\le j_i\\le n_i\\}$ and arc set $$A(Q)=\\cup^t_{i=1}A(H_i)\\cup \\{u_{ij_i}u_{pq_p}\\mid u_iu_p\\in A(T), 1\\le j_i\\le n_i, 1\\le q_p\\le n_p\\}.$$\n  When $T$ is arbitrary, we obtain the following result: every strong digraph com","authors_text":"Gregory Gutin, Yuefang Sun","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2019-06-19T12:18:21Z","title":"Arc-disjoint in- and out-branchings rooted at the same vertex in compositions of digraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.08052","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":"sha256:8fdbd2d0e117c2158537a08f11d0e4b94689d35b7875a976d5ec1e177dd0a902","target":"record","created_at":"2026-05-17T23:42:54Z","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":"4a1653d1af16e2bf6a68a47e7f0edd4c740bd07db6d35722a4657c6b53ea9094","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2019-06-19T12:18:21Z","title_canon_sha256":"d7c5fa3487b7fdd00b45c75ee98a9637a060e44efeba41ff012a784874a3d8e7"},"schema_version":"1.0","source":{"id":"1906.08052","kind":"arxiv","version":1}},"canonical_sha256":"f0de5935157b53af6c8fcf9e4bebc6aaddc9f54ee23b85d7ea08897534f9d39f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0de5935157b53af6c8fcf9e4bebc6aaddc9f54ee23b85d7ea08897534f9d39f","first_computed_at":"2026-05-17T23:42:54.752709Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:54.752709Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0kroxqYB2XCAWQDL0L6pSeURdbHRt4ZwuXb9KSEo1UMs66WzIZsaBhgTbWPWYBLjItywvW+viPBTHxOfsCn7Cg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:54.753300Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.08052","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8fdbd2d0e117c2158537a08f11d0e4b94689d35b7875a976d5ec1e177dd0a902","sha256:4596fa10f2e1fe8dad0e85f69536cee516a8b0de09be5e72990d42cc396dc3d0"],"state_sha256":"449ab50b1801efba0b7e6d6392027b66351c77aaa7a1bfe15aa3d69d47a076f1"}