Coloring Eulerian triangulations of the projective plane

A simple characterization of the 3, 4, or 5-colorable Eulerian triangulations of the projective plane is given. Key words: Projective plane, triangulation, coloring, Eulerian graph. A graph is Eulerian if all its vertices have even degree. It is well known that Eulerian triangulations of the plane are 3-colorable. However, Eulerian triangulations on other surfaces may have arbitrarily large chromatic number. It is easy to find examples on the projective plane whose chromatic number is equal to 3, 4, or 5, respectively, and it is easy to see that the chromatic number of an Eulerian triangulation of the projective plane cannot be more than 5. In this paper we give a simple characterization of when an Eulerian triangulation of the projective plane is 3, 4, or 5-colorable. The class of graphs embedded in some surface S such that all facial walks have even length (called locally bipartite embeddings) is closely related to Eulerian triangulations of S. Namely, if we insert a new vertex in e...

• Type: Journal
• Year: 2002
• Where: DM
• Authors: Bojan Mohar
• Keywords: Chromatic Number, DM 2002, Eulerian Triangulation, Projective Plane