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arXiv · 1507.03975

Generating families of surface triangulations. The case of punctured surfaces with inner degree at least 4

Maria-Jose Chavez·Antonio Quintero·Maria-Trinidad Villar·Seiya Negami
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Abstract

We present two versions of a method for generating all triangulations of any punctured surface in each of these two families: (1) triangulations with inner vertices of degree at least 4 and boundary vertices of degree at least 3 and (2) triangulations with all vertices of degree at least 4. The method is based on a series of reversible operations, termed reductions, which lead to a minimal set of triangulations in each family. Throughout the process the triangulations remain within the corresponding family. Moreover, for the family (1) these operations reduce to the well-known edge contractions and removals of octahedra. The main results are proved by an exhaustive analysis of all possible local configurations which admit a reduction.

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Maria-Jose Chavez, Antonio Quintero, Maria-Trinidad Villar, Seiya Negami. 2015-07-14. Generating families of surface triangulations. The case of punctured surfaces with inner degree at least 4. https://arxiv.org/abs/1507.03975

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