# Generating Maps on Surfaces

@article{Sulanke2017GeneratingMO, title={Generating Maps on Surfaces}, author={Thom Sulanke}, journal={Discrete \& Computational Geometry}, year={2017}, volume={57}, pages={335-356} }

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.

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## References

SHOWING 1-10 OF 12 REFERENCES

### Note on the irreducible triangulations of the Klein bottle

- MathematicsJ. Comb. Theory, Ser. B
- 2006

### Fast generation of planar graphs

- Mathematics
- 2007

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

- Mathematics
- 2006

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

- Mathematics
- 1989

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

- MathematicsJ. Comb. Theory, Ser. B
- 1997

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

### Graphs on Surfaces

- MathematicsJohns Hopkins series in the mathematical sciences
- 2001

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

- MathematicsJ. Algorithms
- 1998

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

- Materials Science
- 1987

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