Five-coloring graphs on the Klein bottle
β Scribed by Nathan Chenette; Luke Postle; Noah Streib; Robin Thomas; Carl Yerger
- Book ID
- 119292663
- Publisher
- Elsevier Science
- Year
- 2012
- Tongue
- English
- Weight
- 554 KB
- Volume
- 102
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
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## Abstract Let __G__ be a graph embedded in the Klein bottle with βrepresentativityβ 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
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