Six-Critical Graphs on the Klein bottle Extended Abstract

We exhibit an explicit list of nine graphs such that a graph drawn in the Klein bottle is 5-colorable if and only if it has no subgraph isomorphic to a member of the list. This answers a question of Thomassen (J. Comb. Theory Ser. B 70 (1997), 67{100) and implies an earlier result of Kr al', Mohar, Nakamoto, Pangr ac and Suzuki that an Eulerian triangulation of the Klein bottle is 5-colorable if and only if it has no complete subgraph on six vertices.