Graph Polynomials: From Recursive Definitions to Subset Expansion Formulas

Many graph polynomials, such as the Tutte polynomial, the interlace polynomial and the matching polynomial, have both a recursive definition and a defining subset expansion formula. In this article, we present a general, logic-based framework which gives a precise meaning to recursive definitions of graph polynomials. We then prove in this framework that every recursive definition of a graph polynomial can be converted into a subset expansion formula.