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 nonorientable) surface of genus g ≥ 0 with b ≥ 0 boundaries 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.

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Alexandre Boulch, Éric Colin de Verdière, Atsuhiro Nakamoto
• Keywords: CORR 2011, Education, Irreducible Triangulation, Surfaces, Triangulation