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From a Zoo to a Zoology: Towards a General Theory of Graph Polynomials

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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 two classes 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.

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  1. Department of Computer Science, Technion–Israel Institute of Technology, Haifa, Israel

    J. A. Makowsky

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Partially supported by a Grant of the Fund for Promotion of Research of the Technion–Israel Institute of Technology.

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Makowsky, J.A. From a Zoo to a Zoology: Towards a General Theory of Graph Polynomials. Theory Comput Syst 43, 542–562 (2008). https://doi.org/10.1007/s00224-007-9022-9

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