Automorphism groups of graphs of bounded Hadwiger number
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866912600251432960 |
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| author | Grohe, Martin Schweitzer, Pascal Wiebking, Daniel |
| author_facet | Grohe, Martin Schweitzer, Pascal Wiebking, Daniel |
| contents | We determine the structure of automorphism groups of finite graphs of bounded Hadwiger number. Our proof includes a structural analysis of finite edge-transitive graphs. In particular, we show that for connected, $K_{h+1}$-minor-free, edge-transitive, twin-free, finite graphs the non-abelian composition factors of the automorphism group have bounded order. We use this to show that the automorphism groups of finite graphs of bounded Hadwiger number are obtained by repeated group extensions using abelian groups, symmetric groups and groups of bounded order. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2012_14300 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Automorphism groups of graphs of bounded Hadwiger number Grohe, Martin Schweitzer, Pascal Wiebking, Daniel Combinatorics Discrete Mathematics Group Theory 05C75, 05C83, 20D60 We determine the structure of automorphism groups of finite graphs of bounded Hadwiger number. Our proof includes a structural analysis of finite edge-transitive graphs. In particular, we show that for connected, $K_{h+1}$-minor-free, edge-transitive, twin-free, finite graphs the non-abelian composition factors of the automorphism group have bounded order. We use this to show that the automorphism groups of finite graphs of bounded Hadwiger number are obtained by repeated group extensions using abelian groups, symmetric groups and groups of bounded order. |
| title | Automorphism groups of graphs of bounded Hadwiger number |
| topic | Combinatorics Discrete Mathematics Group Theory 05C75, 05C83, 20D60 |
| url | https://arxiv.org/abs/2012.14300 |