On the size of k-irreducible triangulations
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866911687167180800 |
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| author | Delecroix, Vincent Fontaine, Oscar de Mesmay, Arnaud |
| author_facet | Delecroix, Vincent Fontaine, Oscar de Mesmay, Arnaud |
| contents | A triangulation of a surface is k-irreducible if every non-contractible curve has length at least k and any edge contraction breaks this property. Equivalently, every edge belongs to a non-contractible curve of length k and there are no shorter non-contractible curves. We prove that a k-irreducible triangulation of an orientable surface of genus g has $O(k^2g)$ triangles, which is optimal. This is an improvement over the previous best bound $k^{O(k)} g^2$ of Gao, Richter and Seymour [Journal of Combinatorial Theory, Series B, 1996]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_20030 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the size of k-irreducible triangulations Delecroix, Vincent Fontaine, Oscar de Mesmay, Arnaud Computational Geometry Discrete Mathematics Combinatorics A triangulation of a surface is k-irreducible if every non-contractible curve has length at least k and any edge contraction breaks this property. Equivalently, every edge belongs to a non-contractible curve of length k and there are no shorter non-contractible curves. We prove that a k-irreducible triangulation of an orientable surface of genus g has $O(k^2g)$ triangles, which is optimal. This is an improvement over the previous best bound $k^{O(k)} g^2$ of Gao, Richter and Seymour [Journal of Combinatorial Theory, Series B, 1996]. |
| title | On the size of k-irreducible triangulations |
| topic | Computational Geometry Discrete Mathematics Combinatorics |
| url | https://arxiv.org/abs/2603.20030 |