2 research outputs found

    The Parameterized Complexity of the Rainbow Subgraph Problem

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    The NP-hard RAINBOW SUBGRAPH problem, motivated from bioinformatics, is to find in an edge-colored graph a subgraph that contains each edge color exactly once and has at most kk vertices. We examine the parameterized complexity of RAINBOW SUBGRAPH for paths, trees, and general graphs. We show that RAINBOW SUBGRAPH  is W[1]-hard with respect to the parameter kk and also with respect to the dual parameter :=nk\ell:=n-k where nn is the number of vertices. Hence, we examine parameter combinations and show, for example, a polynomial-size problem kernel for the combined parameter \ell and ``maximum number of colors incident with any vertex''. Additionally, we show APX-hardness even if the input graph is a properly edge-colored path in which every color occurs at most twice
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