Received: 31 October 2012 / Revised: 13 December 2012 / Accepted: 18 December 2012 / Published: 27 December 2012

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**Abstract**

The problem of finding the maximum number of vertex-disjoint uni-color paths in an edge-colored graph has been recently introduced in literature, motivated by applications in social network analysis. In this paper we investigate the approximation and parameterized complexity of the problem. First,
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The problem of finding the maximum number of vertex-disjoint uni-color paths in an edge-colored graph has been recently introduced in literature, motivated by applications in social network analysis. In this paper we investigate the approximation and parameterized complexity of the problem. First, we show that, for any constant ε > 0, the problem is not approximable within factor c

^{1-ε}, where c is the number of colors, and that the corresponding decision problem is W[1]-hard when parametrized by the number of disjoint paths. Then, we present a fixed-parameter algorithm for the problem parameterized by the number and the length of the disjoint paths. Full article
(This article belongs to the Special Issue Graph Algorithms)