Circle graphs and the automorphism group of the circle
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909455580397568 |
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| author | Georgakopoulos, Agelos |
| author_facet | Georgakopoulos, Agelos |
| contents | We prove that $Aut({\mathbb S}^1)$ coincides with the automorphism group of the \emph{circle graph} $\mathcal{C}$, i.e. the intersection graph of the family of chords of ${\mathbb S}^1$.
We prove that the countable subgraph of $\mathcal{C}$ induced by the rational chords is a strongly universal element of the family of circle graphs, and that it is invariant under local complementation. The only other known connected graphs that have the latter property are $K_2$ and the Rado graph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_07698 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Circle graphs and the automorphism group of the circle Georgakopoulos, Agelos Combinatorics Geometric Topology 05C63, 05C25, 05C10, 05C62, 05E18 We prove that $Aut({\mathbb S}^1)$ coincides with the automorphism group of the \emph{circle graph} $\mathcal{C}$, i.e. the intersection graph of the family of chords of ${\mathbb S}^1$. We prove that the countable subgraph of $\mathcal{C}$ induced by the rational chords is a strongly universal element of the family of circle graphs, and that it is invariant under local complementation. The only other known connected graphs that have the latter property are $K_2$ and the Rado graph. |
| title | Circle graphs and the automorphism group of the circle |
| topic | Combinatorics Geometric Topology 05C63, 05C25, 05C10, 05C62, 05E18 |
| url | https://arxiv.org/abs/2501.07698 |