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From a Zoo to a Zoology: Descriptive Complexity for Graph Polynomials

  • J. A. Makowsky
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3988)

Abstract

We outline a general theory of graph polynomials which covers all the examples we found in the vast literature, in particular, the chromatic polynomial, various generalizations of the Tutte polynomial, matching polynomials, interlace polynomials, and the cover polynomial of digraphs. We introduce the class of (hyper)graph polynomials definable in second order logic, and outline a research program for their classification in terms of definability and complexity considerations, and various notions of reducibilities.

Keywords

Polynomial Time Order Logic Graph Property Recursion Scheme Descriptive Complexity 
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 2006

Authors and Affiliations

  • J. A. Makowsky
    • 1
  1. 1.Department of Computer ScienceTechnion–Israel Institute of TechnologyHaifaIsrael

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