Properties of uniformly $3$-connected graphs
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| Acceso en línea: | |
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| _version_ | 1866929449960734720 |
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| author | Göring, Frank Hofmann, Tobias |
| author_facet | Göring, Frank Hofmann, Tobias |
| contents | A graph on at least ${k+1}$ vertices is uniformly $k$-connected if each pair of its vertices is connected by $k$ and not more than $k$ independent paths. We reinvestigate a recent constructive characterization of uniformly $3$-connected graphs and obtain a more detailed result that relates the number of vertices to the operations involved in constructing a respective uniformly $3$-connected graph. Furthermore, we investigate how crossing numbers and treewidths behave under the mentioned constructions. We demonstrate how these results can be utilized to study the structure and properties of uniformly $3$-connected graphs with minimum number of vertices of minimum degree. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_16966 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Properties of uniformly $3$-connected graphs Göring, Frank Hofmann, Tobias Combinatorics 05C40, 05C75, 05C07, 05D99 A graph on at least ${k+1}$ vertices is uniformly $k$-connected if each pair of its vertices is connected by $k$ and not more than $k$ independent paths. We reinvestigate a recent constructive characterization of uniformly $3$-connected graphs and obtain a more detailed result that relates the number of vertices to the operations involved in constructing a respective uniformly $3$-connected graph. Furthermore, we investigate how crossing numbers and treewidths behave under the mentioned constructions. We demonstrate how these results can be utilized to study the structure and properties of uniformly $3$-connected graphs with minimum number of vertices of minimum degree. |
| title | Properties of uniformly $3$-connected graphs |
| topic | Combinatorics 05C40, 05C75, 05C07, 05D99 |
| url | https://arxiv.org/abs/2211.16966 |