Coloring Groups
Combinatorics
2024-08-07 v4 Group Theory
Abstract
We introduce coloring groups, which are permutation groups obtained from a proper edge coloring of a graph. These groups generalize the generalized toggle groups of Striker (which themselves generalize the toggle groups introduced by Cameron and Fon-der-Flaass). We present some general results connecting the structure of a coloring group to the structure of its graph coloring, providing graph-theoretic characterizations of the centralizer and primitivity of a coloring group. We apply these results particularly to generalized toggle groups arising from trees as well as coloring groups arising from the independence posets introduced by Thomas and Williams.
Keywords
Cite
@article{arxiv.2312.03092,
title = {Coloring Groups},
author = {Ben Adenbaum and Alexander Wilson},
journal= {arXiv preprint arXiv:2312.03092},
year = {2024}
}