Six-Critical Graphs on the Klein Bottle

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 Kral', Mohar, Nakamoto, Pangrac 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.

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