Two characterisations of accessible quasi-transitive graphs
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866913491092242432 |
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| author | Hamann, Matthias Miraftab, Babak |
| author_facet | Hamann, Matthias Miraftab, Babak |
| contents | We prove two characterisations of accessibility of locally finite quasi-transitive connected graphs. First, we prove that any such graph $G$ is accessible if and only if its set of separations of finite order is an ${\rm Aut}(G)$-finitely generated semiring. The second characterisation says that $G$ is accessible if and only if every process of splittings in terms of tree amalgamations stops after finitely many steps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2003_14203 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Two characterisations of accessible quasi-transitive graphs Hamann, Matthias Miraftab, Babak Combinatorics We prove two characterisations of accessibility of locally finite quasi-transitive connected graphs. First, we prove that any such graph $G$ is accessible if and only if its set of separations of finite order is an ${\rm Aut}(G)$-finitely generated semiring. The second characterisation says that $G$ is accessible if and only if every process of splittings in terms of tree amalgamations stops after finitely many steps. |
| title | Two characterisations of accessible quasi-transitive graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2003.14203 |