We determine the complete list of the irreducible triangulations of the Klein bottle, up to equivalence, analyzing their structures. 1997 Academic Press ## 1. Introduction A triangulation of a closed surface is a simple graph embedded on the surface so that each face is triangular and that any tw
Degree-regular triangulations of torus and Klein bottle
β Scribed by Basudeb Datta; Ashish Kumar Upadhyay
- Publisher
- Indian Academy of Sciences
- Year
- 2005
- Tongue
- English
- Weight
- 296 KB
- Volume
- 115
- Category
- Article
- ISSN
- 0253-4142
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
We show how to construct all the graphs that can be embedded on both the torus and the Klein bottle as their triangulations.
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
## Abstract Thomassen conjectured that every longest circuit of a 3βconnected graph has a chord. It is proved in this paper that every longest circuit of a 4βconnected graph embedded in a torus or Klein bottle has a chord. Β© 2003 Wiley Periodicals, Inc. J Graph Theory 43: 1β23, 2003
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