Abstract As a sequel of a previous paper by the authors, we present here a generating theorem for the family of triangulations of an arbitrary punctured surface with vertex degree ≥ 4. The method is based on a series of reversible operations termed reductions which lead to a minimal set of triangulations in such a way that all intermediate triangulations throughout the reduction process remain within the family. Besides contractible edges and octahedra, the reduction operations act on two new configurations near the surface boundary named quasi-octahedra and N-components. It is also observed that another configuration called M-component remains unaltered under any sequence of reduction operations. We show that one gets rid of M-components by flipping appropriate edges.

中文翻译：

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生成度数至少为 4 的穿孔表面三角剖分

摘要作为作者先前论文的续篇，我们在此提出了顶点度≥ 4 的任意穿孔表面的三角剖分族的生成定理。该方法基于称为归约的一系列可逆操作，导致最小的三角剖分集，以使整个归约过程中的所有中间三角剖分都保留在该族中。除了可收缩的边缘和八面体之外，减少操作还作用于表面边界附近的两个新配置，称为准八面体和 N 分量。还观察到另一种称为 M 组件的配置在任何归约操作序列下都保持不变。我们展示了通过翻转适当的边缘来摆脱 M 分量。