Computing the Tutte Polynomial on Graphs of Bounded Clique-Width

  • Omer Giménez
  • Petr Hliněný
  • Marc Noy
Conference paper

DOI: 10.1007/11604686_6

Part of the Lecture Notes in Computer Science book series (LNCS, volume 3787)
Cite this paper as:
Giménez O., Hliněný P., Noy M. (2005) Computing the Tutte Polynomial on Graphs of Bounded Clique-Width. In: Kratsch D. (eds) Graph-Theoretic Concepts in Computer Science. WG 2005. Lecture Notes in Computer Science, vol 3787. Springer, Berlin, Heidelberg

Abstract

The Tutte polynomial is a notoriously hard graph invariant, and efficient algorithms for it are known only for a few special graph classes, like for those of bounded tree-width. The notion of clique-width extends the definition of cograhs (graphs without induced P4), and it is a more general notion than that of tree-width. We show a subexponential algorithm (running in time expO(n2/3)) for computing the Tutte polynomial on cographs. The algorithm can be extended to a subexponential algorithm computing the Tutte polynomial on on all graphs of bounded clique-width. In fact, our algorithm computes the more general U-polynomial.

2000 Math Subjects Classification: 05C85, 68R10.

Keywords

Tutte polynomial cographs clique-width subexponential algorithm U polynomial 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Omer Giménez
    • 1
  • Petr Hliněný
    • 2
  • Marc Noy
    • 1
  1. 1.Department of Applied MathematicsTechnical University of CataloniaBarcelonaSpain
  2. 2.Department of Computer Science, FEITechnical University of OstravaOstravaCzech Republic

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