Characterizing partition functions of the edge-coloring model by rank growth

TL;DR

This paper characterizes which graph invariants can be represented as partition functions of edge-coloring models over complex numbers, using the rank growth of associated connection matrices as a key criterion.

Contribution

It introduces a new characterization of graph invariants as partition functions based on the rank growth of connection matrices, advancing understanding of edge-coloring models.

Findings

Graph invariants are characterized by rank growth conditions.

Connection matrices serve as a tool to identify partition functions.

The work extends the theory of graph invariants and edge-coloring models.

Abstract

We characterize which graph invariants are partition functions of an edge-coloring model over the complex numbers, in terms of the rank growth of associated `connection matrices'.