{"paper":{"title":"Arc-disjoint in- and out-branchings rooted at the same vertex in compositions of digraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Gregory Gutin, Yuefang Sun","submitted_at":"2019-06-19T12:18:21Z","abstract_excerpt":"A digraph $D=(V, A)$ has a good pair at a vertex $r$ if $D$ has a pair of arc-disjoint in- and out-branchings rooted at $r$. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.08052","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"}