On Counting Generalized Colorings

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

Abstract

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 k1, ..., km 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.

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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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