Computing Graph Polynomials on Graphs of Bounded Clique-Width

  • J. A. Makowsky
  • Udi Rotics
  • Ilya Averbouch
  • Benny Godlin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4271)


We discuss the complexity of computing various graph polynomials of graphs of fixed clique-width. We show that the chromatic polynomial, the matching polynomial and the two-variable interlace polynomial of a graph G of clique-width at most k with n vertices can be computed in time O(n f( k)), where f(k) ≤3 for the inerlace polynomial, f(k) ≤2k+1 for the matching polynomial and f(k) ≤3 Open image in new window 2 k + 2 for the chromatic polynomial.


Polynomial Time Characteristic Polynomial Chromatic Number Label Graph Graph Class 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • J. A. Makowsky
    • 1
  • Udi Rotics
    • 2
  • Ilya Averbouch
    • 1
  • Benny Godlin
    • 1
    • 3
  1. 1.Department of Computer ScienceTechnion–Israel Institute of TechnologyHaifaIsrael
  2. 2.School of Computer Science and MathematicsNetanya Academic CollegeNetanyaIsrael
  3. 3.IBM Research and Development LaboratoryHaifaIsrael

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