Generating irreducible triangulations of surfaces

2006/06/27 by T. Sulanke, Thom Sulanke, Sulanke, Thom · 1 citation
Computer Science · Mathematics · #05c10 #05c30 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Commutative Algebra and Its Applications #Computational Geometry and Mesh Generation #FOS: Mathematics #math.CO #msc:05c10 #msc:05c30

paper · pdf · doi:10.48550/arxiv.math/0606687

11 pages

arxiv created 2006/06/27 · openalex publication_date 2006/06/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Starting with the irreducible triangulations of a fixed surface and splitting vertices, all the triangulations of the surface up to a given number of vertices can be generated. The irreducible triangulations have previously been determined for the surfaces S₀, S₁, N₁,and N₂. An algorithm is presented for generating the irreducible triangulations of a fixed surface using triangulations of other surfaces. This algorithm has been implemented as a computer program which terminates for S₁, S₂, N₁, N₂, N₃, and N₄. Thus the complete sets irreducible triangulations are now also known for S₂, N₃, and N₄, with respective cardinalities 396784, 9708, and 6297982.

Citations

• Irreducible triangulations of low genus surfaces
• Triangulated Manifolds with Few Vertices: Combinatorial Manifolds

Cited by

• Isomorphism-free lexicographic enumeration of triangulated surfaces and 3-manifolds

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