Strong digraph compositions with each component size at least 2 have arc-disjoint in- and out-branchings at every vertex; semicomplete compositions are fully characterized for this property.
Bang-Jensen, G
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Arc-disjoint in- and out-branchings rooted at the same vertex in compositions of digraphs
Strong digraph compositions with each component size at least 2 have arc-disjoint in- and out-branchings at every vertex; semicomplete compositions are fully characterized for this property.