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On the Pseudo-achromatic Number Problem

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Graph-Theoretic Concepts in Computer Science (WG 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5344))

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Abstract

We study the parameterized complexity of the pseudo-achromatic number problem: Given an undirected graph and a parameter k, determine if the graph can be partitioned into k groups such that every two groups are connected by at least one edge. This problem has been extensively studied in graph theory and combinatorial optimization. We show that the problem has a kernel of at most (k − 2)(k + 1) vertices that is constructable in time \(O(m\sqrt{n})\), where n and m are the number of vertices and edges, respectively, in the graph, and k is the parameter. This directly implies that the problem is fixed-parameter tractable. We also study generalizations of the problem and show that they are parameterized intractable.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Texas A&M University, College Station, TX 77843, USA

    Jianer Chen, Jie Meng & Fenghui Zhang

  2. School of Computing, DePaul University, Supported by a DePaul University Competitive Research Grant, 243 S. Wabash Avenue, Chicago, IL 60604, USA

    Iyad A. Kanj

  3. Department of Computer Science, Lafayette College, Supported by a Lafayette College Research Grant, Easton, PA 18042, USA

    Ge Xia

Authors
  1. Jianer Chen
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  2. Iyad A. Kanj
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  3. Jie Meng
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  4. Ge Xia
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  5. Fenghui Zhang
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Durham University, South Road, DH1 3LE, Durham, UK

    Hajo Broersma , Tom Friedetzky  & Daniel Paulusma ,  & 

  2. Department of Computer Science, University of Leicester, University Road, LE1 7RH, Leicester, UK

    Thomas Erlebach

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© 2008 Springer-Verlag Berlin Heidelberg

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Chen, J., Kanj, I.A., Meng, J., Xia, G., Zhang, F. (2008). On the Pseudo-achromatic Number Problem. In: Broersma, H., Erlebach, T., Friedetzky, T., Paulusma, D. (eds) Graph-Theoretic Concepts in Computer Science. WG 2008. Lecture Notes in Computer Science, vol 5344. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92248-3_8

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  • DOI: https://doi.org/10.1007/978-3-540-92248-3_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-92247-6

  • Online ISBN: 978-3-540-92248-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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