On the orientable genus of graphs with bounded nonorientable genus
β Scribed by Bojan Mohar
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 396 KB
- Volume
- 182
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
A conjecture of Robertson and Thomas on the orientable genus of graphs with a given nonorientable embedding is disproved.
π SIMILAR VOLUMES
## Abstract Examples are given to show that the nonorientable genus of a graph is not additive over its blocks. A nonorientable analog for the Battle, Harary, Kodama, and Youngs Theorem is proved; this completely determines the nonorientable genus of a graph in terms of its blocks. It is also shown
## Abstract The orientable genus is determined for any graph that embeds into the projective plane, Ξ£, to be essentially half of the representativity of any embedding into Ξ£. In addition, a structure is given for any 3βconnected projective planar graph as the union of a spanning planar graph and a
## 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