In this paper I survey the sources of inspiration for my own and co-authored work in trying to
develop a general theory of graph polynomials. I concentrate on meta-theorems, ie, theorem …

We raise some questions about graph polynomials, highlighting concepts and phenomena
that may merit consideration in the development of a general theory. Our questions are …

Graph polynomials are graph parameters invariant under graph isomorphisms which take
values in a polynomial ring with a fixed finite number of indeterminates. We study graph …

Abstract J. Makowsky and B. Zilber (2004) showed that many variations of graph colorings,
called CP-colorings in the sequel, give rise to graph polynomials. This is true in particular for …

Methods for computing graph polynomials have received considerable attention in the
literature. This chapter discusses a logic-based approach which guarantees efficient …

We study semantic equivalence of multivariate graph polynomials via their distinctive power
introduced in (Makowsky, Ravve, Blanchard 2014) under the name of dp-equivalence …

We survey recent work on the use of Hankel matrices H (f,\Box) for real-valued graph
parameters f and a binary sum-like operation\Box on labeled graphs such as the disjoint …

In this chapter we explore the complexity of exactly computing the Tutte polynomial and its
evaluations for graphs and matroids in various models of computation. The Turing …

Definability and Complexity of Graph Parameters Page 1 Definability and Complexity of
Graph Parameters Johann A. Makowsky Faculty of Computer Science, Technion–Israel …