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The Parameterized Complexity of the Rainbow Subgraph Problem

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Graph-Theoretic Concepts in Computer Science (WG 2014)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 8747))

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Abstract

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”.

Falk Hüffner: Supported by DFG project ALEPH (HU 2139/1).

Christian Komusiewicz: Partially supported by a post-doctorial grant funded by the Région Pays de la Loire.

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Acknowledgments

We thank the reviewers of WG’ 14 for their thorough and valuable feedback.

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Authors and Affiliations

  1. Institut für Softwaretechnik und Theoretische Informatik, TU Berlin, Berlin, Germany

    Falk Hüffner, Christian Komusiewicz, Rolf Niedermeier & Martin Rötzschke

Authors
  1. Falk Hüffner
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  2. Christian Komusiewicz
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  3. Rolf Niedermeier
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  4. Martin Rötzschke
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Corresponding author

Correspondence to Christian Komusiewicz .

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Editors and Affiliations

  1. LITA, Université de Lorraine, Metz Cedex 01, France

    Dieter Kratsch

  2. Université d'Orléans, Orléans, France

    Ioan Todinca

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Hüffner, F., Komusiewicz, C., Niedermeier, R., Rötzschke, M. (2014). The Parameterized Complexity of the Rainbow Subgraph Problem. In: Kratsch, D., Todinca, I. (eds) Graph-Theoretic Concepts in Computer Science. WG 2014. Lecture Notes in Computer Science, vol 8747. Springer, Cham. https://doi.org/10.1007/978-3-319-12340-0_24

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  • DOI: https://doi.org/10.1007/978-3-319-12340-0_24

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-12339-4

  • Online ISBN: 978-3-319-12340-0

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