On Edge-Disjoint Maximal Outerplanar Graphs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917192436547584 |
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| author | Okada, Yuto Otachi, Yota Volk, Lena |
| author_facet | Okada, Yuto Otachi, Yota Volk, Lena |
| contents | We provide two constructions for $t$ edge-disjoint maximal outerplanar graphs on every number of $n \geq 4t$ vertices. The bound on the minimum number of vertices is tight. These constructions yield the existence of optimal outerthickness-$t$ graphs for every $t \in \mathbb{N}$. While one of the constructions works for all values of $t$ and extends graphs from Guy and Nowakowski (1990), the other one holds only for powers of $2$, but yields graphs with maximum degree logarithmic in the number of vertices. Thus, the latter may be helpful in tackling the open question of determining the outerthickness of all complete graphs. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_05885 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Edge-Disjoint Maximal Outerplanar Graphs Okada, Yuto Otachi, Yota Volk, Lena Combinatorics Discrete Mathematics 05C10, 05C70, 68R10 We provide two constructions for $t$ edge-disjoint maximal outerplanar graphs on every number of $n \geq 4t$ vertices. The bound on the minimum number of vertices is tight. These constructions yield the existence of optimal outerthickness-$t$ graphs for every $t \in \mathbb{N}$. While one of the constructions works for all values of $t$ and extends graphs from Guy and Nowakowski (1990), the other one holds only for powers of $2$, but yields graphs with maximum degree logarithmic in the number of vertices. Thus, the latter may be helpful in tackling the open question of determining the outerthickness of all complete graphs. |
| title | On Edge-Disjoint Maximal Outerplanar Graphs |
| topic | Combinatorics Discrete Mathematics 05C10, 05C70, 68R10 |
| url | https://arxiv.org/abs/2601.05885 |