This article is cited in 1 paper

Discrete mathematics and mathematical cybernetics

Irreducible triangulations of the once-punctured torus

S. Lawrencenko^a, T. Sulanke^b, M. T. Villar^c, L. V. Zgonnik^a, M. J. Chávez^c, J. R. Portillo<sup>c

a</sup> Russian State University of Tourism and Service, Institute for Tourism and Hospitality, Kronstadt Boulevard, 32A, Moscow, 125438, Russia
^b Department of Physics, Indiana University, Bloomington, Indiana 47405, USA
^c Universidad de Sevilla, Sevilla, Spain

Abstract: 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.

Keywords: triangulation of 2-manifold, irreducible triangulation, 2-manifold with boundary, punctured torus.

UDC: 519.1

MSC: 57M15

Received March 5, 2016, published March 19, 2018

Language: English

DOI: 10.17377/semi.2018.15.026

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