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arXiv · 2312.03092

Coloring Groups

Ben Adenbaum·Alexander Wilson
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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.

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Ben Adenbaum, Alexander Wilson. 2023-12-05. Coloring Groups. https://doi.org/10.46298/dmtcs.12753

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