Generating Maps on Surfaces

  title={Generating Maps on Surfaces},
  author={Thom Sulanke},
  journal={Discrete \& Computational Geometry},
  • T. Sulanke
  • Published 21 September 2015
  • Mathematics
  • Discrete & Computational Geometry
We describe procedures for generating all 2-cell embedded simple graphs with up to a fixed number of vertices on a given surface. We also modify these procedures to generate closed 2-cell embeddings and polyhedral embeddings. We give results of computer implementations of these procedures for seven surfaces: the sphere, the torus, the double torus, the projective plane, the Klein bottle, the triple cross surface, and the quadruple cross surface. 

A generating theorem of punctured surface triangulations with inner degree at least 4

Abstract Given any punctured surface F2, we present a method for generating all of F2 triangulations with inner vertices of degree ≥ 4 and boundary vertices of degree ≥ 3. The method is based on a

The Optimal Packing of Eight Points in the Real Projective Plane

The contact graph of the putatively optimal numerical packing of Conway, Hardin and Sloane is the only graph that survives, and from this graph an exact expression for the minimum distance of eight optimally packed points in the real projective plane is recovered.

Digital Terrain Model Geospatial Modelling

The modelling means the world object cognition based on the analogy. This analogy presents an idea and material imitation of some properties of the existing world. It is processed by various



Generating the triangulations of the projective plane

Fast generation of planar graphs

The program plantri is the fastest isomorph-free generator of many classes of planar graphs, including triangulations, quadrangulations, and convex polytopes. Many applications in the natural

Generating irreducible triangulations of surfaces

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

All 2-manifolds have finitely many minimal triangulations

A triangulation of a 2-manifoldM is said to be minimal provided one cannot produce a triangulation ofM with fewer vertices by shrinking an edge. In this paper we prove that all 2-manifolds have

Irreducible Triangulations of the Klein Bottle

The complete list of the irreducible triangulations of the Klein bottle, up to equivalence, analyzing their structures is determined.

Graph minors. VII. Disjoint paths on a surface

Graphs on Surfaces

This chapter discusses Embeddings Combinatorially, Contractibility, of Cycles, and the Genus Problem, which focuses on planar graphs and the Jordan Curve Theorem, and colorings of Graphs on Surfaces, which are 5-choosable.

Isomorph-Free Exhaustive Generation

We describe a very general technique for generating families of combinatorial objects without isomorphs. It applies to almost any class of objects for which an inductive construction process exists.

Irreducible triangulations of a torus

A polyurethane foam which absorbs impact effectively is prepared by cross-linking short chain polyol to high polymer polyol chains by using polyisocyanate.