Irreducible Triangulations of Surfaces with Boundary
Irreducible Triangulations of Surfaces with Boundary
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DOI：
10.1007/s00373-012-1244-1
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发表时间：
2011-03
影响因子：
0.7
通讯作者：
Alexandre Boulch;Éric Colin de Verdière;Atsuhiro Nakamoto
中科院分区：
文献类型：
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作者：
Alexandre Boulch;Éric Colin de Verdière;Atsuhiro Nakamoto
一个曲面的三角剖分是不可约的，如果没有边可以收缩以产生同一曲面的三角剖分。本文研究了带边界曲面的不可约三角剖分问题。证明了亏格g ≥ 0的曲面（可能不可定向）的不可约三角剖分的顶点数为O（g+B），边界分支为B ≥ 0.到目前为止，该结果仅对无边界曲面（B= 0）已知。虽然我们的技术在O（.）符号，目前的证明是初等的，和简单的比以前的情况下，曲面无边界。
A triangulation of a surface isirreducibleif 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 genusg≥ 0 withb≥ 0 boundary components isO(g+b). So far, the result was known only for surfaces without boundary (b= 0). While our technique yields a worse constant in theO(.) notation, the present proof is elementary, and simpler than the previous ones in the case of surfaces without boundary.