Meta-theorems for Graph Polynomials

TL;DR

This paper surveys the development of a general theory of graph polynomials through meta-theorems that depend on formal properties rather than specific definitions.

Contribution

It introduces the concept of meta-theorems for graph polynomials, emphasizing formal properties over particular polynomial definitions.

Findings

Meta-theorems depend only on formal properties of graph polynomial classes.

The approach unifies various graph polynomial results under a common framework.

Provides inspiration for future research in graph polynomial theory.

Abstract

In this paper I survey the sources of inspiration for my own and co-authored work in trying to develop a general theory of graph polynomials. I concentrate on meta-theorems, i.e., theorem which depend only on the form infinite classes of graph polynomials are defined in some formalism, and not on the actual meaning of the particular definitions.