A note on recognizing an old friend in a new place: list coloring and the zero-temperature Potts model

TL;DR

This paper establishes a connection between list coloring in graph theory and the zero-temperature antiferromagnetic Potts model with an external field, providing a new polynomial that equals the partition function and opening avenues for cross-disciplinary research.

Contribution

It introduces a list coloring polynomial that matches the partition function of the zero-temperature Potts model, bridging graph theory and statistical physics.

Findings

List coloring polynomial equals the Potts model partition function.

Connection extends the chromatic polynomial's analogy to the Potts model.

Suggests new research directions in both graph theory and statistical physics.

Abstract

Here we observe that list coloring in graph theory coincides with the zero-temperature antiferromagnetic Potts model with an external field. We give a list coloring polynomial that equals the partition function in this case. This is analogous to the well-known connection between the chromatic polynomial and the zero-temperature, zero-field, antiferromagnetic Potts model. The subsequent cross fertilization yields immediate results for the Potts model and suggests new research directions in list coloring.