Characterising 4-tangles through a connectivity property
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866916781409435648 |
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| author | Carmesin, Johannes Kurkofka, Jan |
| author_facet | Carmesin, Johannes Kurkofka, Jan |
| contents | Every large $k$-connected graph-minor induces a $k$-tangle in its ambient graph. The converse holds for $k\le 3$, but fails for $k\ge 4$. This raises the question whether `$k$-connected' can be relaxed to obtain a characterisation of $k$-tangles through highly cohesive graph-minors. We show that this can be achieved for $k=4$ by proving that internally 4-connected graphs have unique 4-tangles, and that every graph with a 4-tangle $τ$ has an internally 4-connected minor whose unique 4-tangle lifts to $τ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_00902 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Characterising 4-tangles through a connectivity property Carmesin, Johannes Kurkofka, Jan Combinatorics Discrete Mathematics 05C83 (Primary), 05C40, 05C05, 05C10 (Secondary) Every large $k$-connected graph-minor induces a $k$-tangle in its ambient graph. The converse holds for $k\le 3$, but fails for $k\ge 4$. This raises the question whether `$k$-connected' can be relaxed to obtain a characterisation of $k$-tangles through highly cohesive graph-minors. We show that this can be achieved for $k=4$ by proving that internally 4-connected graphs have unique 4-tangles, and that every graph with a 4-tangle $τ$ has an internally 4-connected minor whose unique 4-tangle lifts to $τ$. |
| title | Characterising 4-tangles through a connectivity property |
| topic | Combinatorics Discrete Mathematics 05C83 (Primary), 05C40, 05C05, 05C10 (Secondary) |
| url | https://arxiv.org/abs/2309.00902 |