6-Critical Graphs on the Klein Bottle
Ken‐ichi Kawarabayashi, Daniel Král͏̌, Jan Kynčl, Bernard Lidický · SIAM Journal on Discrete Mathematics · 2009
We provide a complete list of 6-critical graphs that can be embedded on the Klein bottle settling a problem of Thomassen [J. Combin. Theory Ser. B, 70 (1997), pp. 67–100, Problem 3]. The list consists of nine nonisomorphic graphs which have altogether 18 nonisomorphic 2-cell embeddings and one embedding that is not 2-cell.