$K_6$-Minors in Triangulations on the Klein Bottle
β Scribed by Kawarabayashi, Ken-ichi; Mukae, Raiji; Nakamoto, Atsuhiro
- Book ID
- 118196997
- Publisher
- Society for Industrial and Applied Mathematics
- Year
- 2009
- Tongue
- English
- Weight
- 238 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0895-4801
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## Abstract In this paper, we shall prove that a projectiveβplanar (resp., toroidal) triangulation __G__ has __K__~6~ as a minor if and only if __G__ has no quadrangulation isomorphic to __K__~4~ (resp., __K__~5~ ) as a subgraph. As an application of the theorems, we can prove that Hadwiger's conje
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