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The 2-Extendability of Graphs on the Projective Plane, the Torus and the Klein Bottle

โœ Scribed by Iwao Mizukai; Seiya Negami; Yusuke Suzuki

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

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๐Ÿ“œ SIMILAR VOLUMES

Disjoint Cycles in Directed Graphs on th
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โœ G.L. Ding; A. Schrijver; P.D. Seymour ๐Ÿ“‚ Article ๐Ÿ“… 1993 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 203 KB

We give necessary and sufficient conditions for a directed graph embedded on the torus or the Klein bottle to contain pairwise disjoint circuits, each of a given orientation and homotopy, and in a given order. For the Klein bottle, the theorem is new. For the torus, the theorem was proved before by

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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