Graph Polynomials: From Recursive Definitions To Subset Expansion Formulas

Details Graph Polynomials: From Recursive Definitions To Subset Expansion Formulas Graph Polynomials: From Recursive Definitions To Subset Expansion Formulas

2008-12-07

arxiv.org/abs/0812.1364v1

Computer Science

Logic in Computer Science

25 pages, 2 figures

Scientific paper

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.

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