Coloring Groups
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916347889319936 |
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| author | Adenbaum, Ben Wilson, Alexander |
| author_facet | Adenbaum, Ben Wilson, Alexander |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_03092 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Coloring Groups Adenbaum, Ben Wilson, Alexander Combinatorics Group Theory 05E18, 06A75, 05C25 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. |
| title | Coloring Groups |
| topic | Combinatorics Group Theory 05E18, 06A75, 05C25 |
| url | https://arxiv.org/abs/2312.03092 |