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arXiv · 2603.20030

On the size of k-irreducible triangulations

Vincent Delecroix·Oscar Fontaine·Arnaud de Mesmay
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Abstract

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].

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Vincent Delecroix, Oscar Fontaine, Arnaud de Mesmay. 2026-03-20. On the size of k-irreducible triangulations. https://arxiv.org/abs/2603.20030

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