Ben Adenbaum ; Alexander Wilson - Coloring Groups

dmtcs:12753 - Discrete Mathematics & Theoretical Computer Science, July 7, 2024, vol. 26:2 - https://doi.org/10.46298/dmtcs.12753
Coloring GroupsArticle

Authors: Ben Adenbaum ORCID; Alexander Wilson

    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.


    Volume: vol. 26:2
    Section: Combinatorics
    Published on: July 7, 2024
    Accepted on: May 7, 2024
    Submitted on: December 28, 2023
    Keywords: Mathematics - Combinatorics,Mathematics - Group Theory,05E18, 06A75, 05C25

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