Journal of Graph Theory最新文献

An out-branching $��B_u^{+}�$ (in-branching $��B_u^{-}�$) in a digraph $��D�$ is a connected spanning subdigraph of $��D�$ in which every vertex except the vertex $��u�$, called the root, has in-degree (out-degree) one. It is well known that there exists a polynomial algorithm for deciding whether a given digraph has $��k�$ arc-disjoint out-branchings with prescribed roots ($��k�$ is part of the input). In sharp contrast to this, it is already NP-complete to decide if a digraph has one out-branching which is arc-disjoint from some in-branching. A digraph is semicomplete if it has no pair of nonadjacent vertices. A tournament is a semicomplete digraph without directed cycles of length 2. In this paper we give a complete classification of semicomplete digraphs that have an out-branching $��B_u^{+}�$ which is arc-disjoint from some in-branching