Coloring Eulerian triangulations of the Klein bottle

Abstract

We show that an Eulerian triangulation of the Klein bottle has chromatic number equal to six if and only if it contains a complete graph of order six, and it is 5-colorable, otherwise. As a consequence of our proof, we derive that every Eulerian triangulation of the Klein bottle with face-width at least four is 5-colorable.

Keywords

• Eulerian trinagulation
• Klein bottle
• face-width