Spanning plane subgraphs of $1$-plane graphs
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911830528491520 |
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| author | Noguchi, Kenta Ota, Katsuhiro Suzuki, Yusuke |
| author_facet | Noguchi, Kenta Ota, Katsuhiro Suzuki, Yusuke |
| contents | A graph drawn on the plane is called $1$-plane if each edge is crossed at most once by another edge. In this paper, we show that every $4$-connected $1$-plane graph has a connected spanning plane subgraph. We also show that there exist infinitely many $4$-connected $1$-plane graphs that have no $2$-connected spanning plane subgraphs. Moreover, we consider the condition of $k$ and $l$ such that every $k$-connected $1$-plane graph has an $l$-connected spanning plane subgraph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_05394 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spanning plane subgraphs of $1$-plane graphs Noguchi, Kenta Ota, Katsuhiro Suzuki, Yusuke Combinatorics 05C10, 05C70 A graph drawn on the plane is called $1$-plane if each edge is crossed at most once by another edge. In this paper, we show that every $4$-connected $1$-plane graph has a connected spanning plane subgraph. We also show that there exist infinitely many $4$-connected $1$-plane graphs that have no $2$-connected spanning plane subgraphs. Moreover, we consider the condition of $k$ and $l$ such that every $k$-connected $1$-plane graph has an $l$-connected spanning plane subgraph. |
| title | Spanning plane subgraphs of $1$-plane graphs |
| topic | Combinatorics 05C10, 05C70 |
| url | https://arxiv.org/abs/2404.05394 |