6-Critical Graphs on the Klein Bottle

Authors:
Ken-ichi Kawarabayashi;Daniel Král';Jan Kynčl;Bernard Lidický
Affiliations:
k_keniti@nii.ac.jp;kral@kam.mff.cuni.cz;kyncl@kam.mff.cuni.cz;bernard@kam.mff.cuni.cz
Venue:
SIAM Journal on Discrete Mathematics
Year:
2009

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5-Coloring Graphs with 4 Crossings

SIAM Journal on Discrete Mathematics
Five-coloring graphs on the Klein bottle

Journal of Combinatorial Theory Series B

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Abstract

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.