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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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