图多项式：从递归定义到子集展开公式
Graph Polynomials: From Recursive Definitions To Subset Expansion Formulas
摘要：
许多图多项式，如Tutte多项式，交织多项式和匹配多项式，都有递归定义和定义子集展开公式。在本文中，我们提出了一个通用的，基于逻辑的框架，它给出了一个精确的意义，递归定义的图多项式。然后，我们证明，在这个框架中，每一个递归定义的图多项式可以转换成一个子集的扩展公式。
英文摘要：
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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