Min-1-Planarity is NP-Hard
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866918517302886400 |
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| author | Okada, Yuto |
| author_facet | Okada, Yuto |
| contents | In this paper, we show that it is NP-hard to determine whether a given graph admits a min-1-planar drawing. A drawing of a graph is min-$k$-planar if, for every crossing in the drawing, at least one of the two crossing edges involves at most $k$ crossings. This notion of min-$k$-planarity was introduced by Binucci, Büngener, Di Battista, Didimo, Dujmović, Hong, Kaufmann, Liotta, Morin, and Tappini [GD 2023; JGAA, 2024] as a generalization of $k$-planarity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_14834 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Min-1-Planarity is NP-Hard Okada, Yuto Computational Geometry Data Structures and Algorithms In this paper, we show that it is NP-hard to determine whether a given graph admits a min-1-planar drawing. A drawing of a graph is min-$k$-planar if, for every crossing in the drawing, at least one of the two crossing edges involves at most $k$ crossings. This notion of min-$k$-planarity was introduced by Binucci, Büngener, Di Battista, Didimo, Dujmović, Hong, Kaufmann, Liotta, Morin, and Tappini [GD 2023; JGAA, 2024] as a generalization of $k$-planarity. |
| title | Min-1-Planarity is NP-Hard |
| topic | Computational Geometry Data Structures and Algorithms |
| url | https://arxiv.org/abs/2605.14834 |