A Complete Characterisation of the Linear Clique-Width of Path Powers

  • Pinar Heggernes
  • Daniel Meister
  • Charis Papadopoulos
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5532)


A k-path power is the k-power graph of a simple path of arbitrary length. Path powers form a non-trivial subclass of proper interval graphs. Their clique-width is not bounded by a constant, and no polynomial-time algorithm is known for computing their clique-width or linear clique-width. We show that k-path powers above a certain size have linear clique-width exactly k + 2, providing the first complete characterisation of the linear clique-width of a graph class of unbounded clique-width. Our characterisation results in a simple linear-time algorithm for computing the linear clique-width of all path powers.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Pinar Heggernes
    • 1
  • Daniel Meister
    • 1
  • Charis Papadopoulos
    • 2
  1. 1.Department of InformaticsUniversity of BergenNorway
  2. 2.Department of MathematicsUniversity of IoanninaGreece

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