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. By implementing the algorithm on computer, we have found a list of 297 nonisomorphic combinatorial types of irreducible triangulations on the once-punctured torus. 
Mar\'ia Jos\'e Ch\'avez and Serge Lawrencenko and Jos\'e Ram\'on   Portillo and Mar\'ia Trinidad Villar
math.CO