Irreducible triangulations of the Möbius band

A complete list of irreducible triangulations is identified on the Möbius band.Plan Andaluz de Investigación (Junta de Andalucía)Ministerio de Ciencia e Innovació

Irreducible triangulations of the once-punctured torus

A triangulation of a surface with fixed topological type is called irreducible if no edge can be contracted to a vertex while remaining in the category of simplicial complexes and preserving the topology of the surface. A complete list of combinatorial structures of irreducible triangulations is made by hand for the once-punctured torus, consisting of exactly 297 non-isomorphic triangulations.Plan Andaluz de Investigación (Junta de Andalucía)Ministerio de Ciencia e Innovació

An algorithm that constructs irreducible triangulations of once-punctured surfaces

A triangulation of a surface is irreducible if there is no edge whose contraction produces another triangulation of the surface. In this work we propose an algorithm that constructs the set of irreducible triangulations of any surface with precisely one boundary component.Plan Andaluz de Investigación (Junta de Andalucía