Graph Polynomials: From Recursive Definitions To Subset Expansion Formulas

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Godlin, Benny
Katz, Emilia
Makowsky, Johann A.
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Abstract
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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.
Comment: 25 pages, 2 figures
Keywords
Computer Science - Logic in Computer Science, Computer Science - Discrete Mathematics
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