The Parameterized Complexity of the Rainbow Subgraph Problem

  • Falk Hüffner
  • Christian KomusiewiczEmail author
  • Rolf Niedermeier
  • Martin Rötzschke
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8747)


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 \(k\) vertices. We examine the parameterized complexity of Rainbow Subgraph for paths, trees, and general graphs. We show, for example, APX-hardness even if the input graph is a properly edge-colored path in which every color occurs at most twice. Moreover, we show that Rainbow Subgraph is W[1]-hard with respect to the parameter \(k\) and also with respect to the dual parameter \(\ell :=n-k\) where \(n\) 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”.


Input Graph Edge Color Minimum Vertex Cover Dual Parameter Maximum Vertex Degree 
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We thank the reviewers of WG’ 14 for their thorough and valuable feedback.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Falk Hüffner
    • 1
  • Christian Komusiewicz
    • 1
    Email author
  • Rolf Niedermeier
    • 1
  • Martin Rötzschke
    • 1
  1. 1.Institut für Softwaretechnik und Theoretische InformatikTU BerlinBerlinGermany

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