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Edge-disjoint paths in digraphs with bounded independence number. (English) Zbl 1302.05067
Summary: A digraph $$H$$ is infused in a digraph $$G$$ if the vertices of $$H$$ are mapped to vertices of $$G$$ (not necessarily distinct), and the edges of $$H$$ are mapped to edge-disjoint directed paths of $$G$$ joining the corresponding pairs of vertices of $$G$$. The algorithmic problem of determining whether a fixed graph $$H$$ can be infused in an input graph $$G$$ is polynomial-time solvable for all graphs $$H$$ (using paths instead of directed paths). However, the analogous problem in digraphs is NP-complete for most digraphs $$H$$. We provide a polynomial-time algorithm to solve a rooted version of the problem, for all digraphs $$H$$, in digraphs with independence number bounded by a fixed integer $$\alpha$$. The problem that we solve is a generalization of the $$k$$ edge-disjoint directed paths problem (for fixed $$k$$).

##### MSC:
 05C20 Directed graphs (digraphs), tournaments 05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) 05C85 Graph algorithms (graph-theoretic aspects)
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