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  "path": "/abs/2603.20030v1",
  "publishedAt": "2026-03-23T00:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "Vincent Delecroix",
    "Oscar Fontaine",
    "Arnaud de Mesmay"
  ],
  "textContent": "**Authors:** Vincent Delecroix, Oscar Fontaine, Arnaud de Mesmay\n\nA 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 a 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"
}