Graph Polynomials: From Recursive Definitions To Subset Expansion Formulas

Abstract

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 paper we present a general, logic-based framework which gives a precise meaning to recursive definitions of graph polynomials. We then prove that in this framework every recursive definition of a graph polynomial can be converted into a subset expansion formula.

25 pages, 2 figures

References in corpus (1)

• The multivariate Tutte polynomial (alias Potts model) for graphs and matroids

Cited by in corpus (1)

• The Enumeration of Vertex Induced Subgraphs with respect to the Number of Components