English

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

Combinatorics 2015-02-25 v3 Statistical Mechanics

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.

Keywords

Cite

@article{arxiv.1406.5532,
  title  = {A note on recognizing an old friend in a new place: list coloring and the zero-temperature Potts model},
  author = {Joanna A. Ellis-Monaghan and Iain Moffatt},
  journal= {arXiv preprint arXiv:1406.5532},
  year   = {2015}
}