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Drawing Disconnected Graphs on the Klein Bottle

✍ Scribed by Laurent Beaudou; Antoine Gerbaud; Roland Grappe; Frédéric Palesi


Publisher
Springer Japan
Year
2010
Tongue
English
Weight
140 KB
Volume
26
Category
Article
ISSN
0911-0119

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📜 SIMILAR VOLUMES


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## Abstract Let __G__ be a graph embedded in the Klein bottle with “representativity” at least four. We give a formula for the orientable genus of __G__, which also implies a polynomially bounded algorithm. The formula is in terms of the number of times certain closed curves on the Klein bottle int

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There are two main purposes of this article. First we show that every 3-connected graph embedded in the torus or the Klein bottle has a spanning planar subgraph which is 2-connected, and in fact has a slightly stronger connectivity property. Second, this subgraph is applied to show that every 3-conn