Geodesic
Coloring Groups
Discrete mathematics & theoretical computer science, Tome 26 (2024) no. 2.

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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.
DOI : 10.46298/dmtcs.12753
Classification : 05C15, 05C25, 06A07 
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     title = {Coloring {Groups}},
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Adenbaum, Ben; Wilson, Alexander. Coloring Groups. Discrete mathematics & theoretical computer science, Tome 26 (2024) no. 2. doi : 10.46298/dmtcs.12753. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.12753/

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