On Counting Generalized Colorings

  • T. Kotek
  • J. A. Makowsky
  • B. Zilber
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5213)


It is well known that the number of proper k-colorings of a graph is a polynomial in k. We investigate in this talk under what conditions a numeric graph invariant which is parametrized with parameters k 1, ..., k m is a polynomial in these parameters. We give a sufficient conditions for this to happen which is general enough to encompass all the graph polynomials which are definable in Second Order Logic. This not only covers the various generalizations of the Tutte polynomials, Interlace polynomials, Matching polynomials, but allows us to identify new graph polynomials related to combinatorial problems discussed in the literature.


Generalize Coloring Extension Property Counting Function Vertex Coloring Tutte Polynomial 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • T. Kotek
    • 1
  • J. A. Makowsky
    • 1
  • B. Zilber
    • 2
  1. 1.Department of Computer ScienceTechnion-Israel Institute of TechnologyHaifaIsrael
  2. 2.Mathematical InstituteUniversity of Oxford 

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