Excluding disjoint Kuratowski graphs
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917661873537024 |
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| author | Robertson, Neil Seymour, Paul |
| author_facet | Robertson, Neil Seymour, Paul |
| contents | A graph is a ``$k$-Kuratowski graph'' if it has exactly $k$ components, each isomorphic to $K_5$ or to $K_{3,3}$. We prove that if a graph $G$ contains no $k$-Kuratowski graph as a minor,then there is a set $X$ of boundedly many vertices such that $G\setminus X$ can be drawn in a (possibly disconnected) surface in which no $k$-Kuratowski graph can be drawn. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_05381 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Excluding disjoint Kuratowski graphs Robertson, Neil Seymour, Paul Combinatorics 05C10, 05C62, 05C83 A graph is a ``$k$-Kuratowski graph'' if it has exactly $k$ components, each isomorphic to $K_5$ or to $K_{3,3}$. We prove that if a graph $G$ contains no $k$-Kuratowski graph as a minor,then there is a set $X$ of boundedly many vertices such that $G\setminus X$ can be drawn in a (possibly disconnected) surface in which no $k$-Kuratowski graph can be drawn. |
| title | Excluding disjoint Kuratowski graphs |
| topic | Combinatorics 05C10, 05C62, 05C83 |
| url | https://arxiv.org/abs/2405.05381 |