Jones' conjecture for Halin graphs and a bit more
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910034957434880 |
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| author | Bärnkopf, Pál Győri, Ervin |
| author_facet | Bärnkopf, Pál Győri, Ervin |
| contents | We prove Jones' famous conjecture for Halin graphs and a somewhat more general class of graphs, too. A based planar graph is a planar one that has a face adjacent to every other face. We confirm Jones' conjecture for based planar graphs. Namely, if a based planar graph does not contain $k+1$ vertex-disjoint cycles, then it suffices to delete $2k$ vertices to make it acyclic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_07376 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Jones' conjecture for Halin graphs and a bit more Bärnkopf, Pál Győri, Ervin Combinatorics We prove Jones' famous conjecture for Halin graphs and a somewhat more general class of graphs, too. A based planar graph is a planar one that has a face adjacent to every other face. We confirm Jones' conjecture for based planar graphs. Namely, if a based planar graph does not contain $k+1$ vertex-disjoint cycles, then it suffices to delete $2k$ vertices to make it acyclic. |
| title | Jones' conjecture for Halin graphs and a bit more |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2401.07376 |