Irreducible triangulations of surfaces with boundary
Combinatorics
2013-11-05 v2 Discrete Mathematics
Abstract
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 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.
Keywords
Cite
@article{arxiv.1103.5364,
title = {Irreducible triangulations of surfaces with boundary},
author = {Alexandre Boulch and Éric Colin de Verdière and Atsuhiro Nakamoto},
journal= {arXiv preprint arXiv:1103.5364},
year = {2013}
}