Minor-minimal 6-regular graphs in the Klein bottle

Authors:
Gašper Fijavž
Affiliations:
Institute of Mathematics, Physics, and Mechanics, Jadranska 19, Ljubljana, Slovenia, Faculty of Computer and Information Science, University of Ljubljana, Tržaška 25, Ljubljana, Slovenia
Venue:
European Journal of Combinatorics - Special issue: Topological graph theory
Year:
2004

Citing 4
Cited 1

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Graph Theory With Applications

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Abstract

Let K6 denote the class of all 6-regular graphs which admit an embedding into the Klein bottle. Using the characterization of graphs in K6 we find minor minimal graphs in K6. As a corollary we show that (i) every 6-regular Klein bottlal graph contains a 6-connected minor, and (ii) no 6-regular graph admits an embedding in both the torus and the Klein bottle.