Generating Even Triangulations on the Klein Bottle

We define two reductions a 4-contradiction and a 2-removal for even triangulation on a surface. It is well known that these reductions preserve some properties of graphs. The complete lists of minimal even triangulations for the sphere, the projective plane and the torus with respect to these reductions have been already determined. In this paper, we make the complete list of minimal even triangulations of the Klein bottle and prove some applications by checking the list.