6-Critical Graphs on the Klein Bottle
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.
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Copyright © 2009 Society for Industrial and Applied Mathematics.
History
Submitted: 30 October 2007
Accepted: 9 September 2008
Published online: 14 January 2009
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