Penrose P2 Tilings: A Study of Fully Leafed Induced Subtrees
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915851710496768 |
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| author | Cloutier, Mathieu Goupil, Alain Massé, Alexandre Blondin |
| author_facet | Cloutier, Mathieu Goupil, Alain Massé, Alexandre Blondin |
| contents | We present new results about fully leafed induced subtrees in Penrose P2 tilings. We first determine the graph structure of these subtrees and show that they are caterpillars, up to an appendix of at most six tiles. We then study bi-infinite fully leafed induced caterpillars in P2 tilings and their geometric properties. In particular, we refute the conjecture proposed by C. Porrier, A. Goupil and A. Blondin Massé that there is a unique bi-infinite fully leafed caterpillar in Penrose P2 tilings. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_10172 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Penrose P2 Tilings: A Study of Fully Leafed Induced Subtrees Cloutier, Mathieu Goupil, Alain Massé, Alexandre Blondin Combinatorics 05C35 (Primary) 52C23, 90C27, 05C63, 05C05, 52C20, 05B45 (Secondary) We present new results about fully leafed induced subtrees in Penrose P2 tilings. We first determine the graph structure of these subtrees and show that they are caterpillars, up to an appendix of at most six tiles. We then study bi-infinite fully leafed induced caterpillars in P2 tilings and their geometric properties. In particular, we refute the conjecture proposed by C. Porrier, A. Goupil and A. Blondin Massé that there is a unique bi-infinite fully leafed caterpillar in Penrose P2 tilings. |
| title | Penrose P2 Tilings: A Study of Fully Leafed Induced Subtrees |
| topic | Combinatorics 05C35 (Primary) 52C23, 90C27, 05C63, 05C05, 52C20, 05B45 (Secondary) |
| url | https://arxiv.org/abs/2603.10172 |