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Journal Articles Graphs and Combinatorics Year : 2013

Irreducible Triangulations of Surfaces with Boundary


A triangulation of a surface is irreducible if no edge can be contracted to produce a triangulation of the same surface. In this paper, we investigate irreducible triangulations of surfaces with boundary. We prove that the number of vertices of an irreducible triangulation of a (possibly non-orientable) surface of genus g ≥ 0 with b ≥ 0 boundary components is O(g + b). So far, the result was known only for surfaces without boundary (b = 0). While our technique yields a worse constant in the O(.) notation, the present proof is elementary, and simpler than the previous ones in the case of surfaces without boundary.
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hal-01163747 , version 1 (16-06-2015)



Alexandre Boulch, Éric Colin de Verdière, Atsuhiro Nakamoto. Irreducible Triangulations of Surfaces with Boundary. Graphs and Combinatorics, 2013, 29 (6), pp.1675-1688. ⟨10.1007/s00373-012-1244-1⟩. ⟨hal-01163747⟩
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