# On irreducible triangulations of punctured and pinched surfaces

@article{Chavez2012OnIT, title={On irreducible triangulations of punctured and pinched surfaces}, author={M. J. Ch'avez and Serge Lawrencenko and Antonio Quintero and I M.T.VillarDepartamentodeMatem'aticaAplicada and Universidad de Sevilla and Sevilla and Spain. and 1 DepartmentofHigherMathematics and National Research University of Electronic Technology and Zelenograd and Russia. and Departamento de Geometr'ia y Topolog'ia}, journal={arXiv: Combinatorics}, year={2012} }

A triangulation of a punctured or pinched surface is irreducible if no edge can be shrunk without producing multiple edges or changing the topological type of the surface. The finiteness of the set of (non-isomorphic) irreducible triangulations of any punctured surface is established. Complete lists of irreducible triangulations are determined for the M\"obius band (6 in number) and the pinched torus (2 in number). All the non-isomorphic combinatorial types (20 in number) of triangulations of…

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