5-Chromatic even triangulations on surfaces

A triangulation is said to be even if each vertex has even degree. It is known that every even triangulation on any orientable surface with sufficiently large representativity is 4-colorable J. Hutchinson, B. Richter, P. Seymour, Colouring Eulerian triangulations, J. Combin. Theory, Ser. B 84 (2002) 225-239], but all graphs on any surface with large representativity are 5-colorable C. Thomassen, Five-coloring maps on surfaces, J. Combin Theory Ser. B 59 (1993) 89-105]. In this paper, we shall characterize 5-chromatic even triangulations with large representativity, which appear only on nonorientable surfaces.