On the Nonembeddability and Crossing Numbers of Some Kleinical Polyhedral Maps on the Torus
โ Scribed by Adrian Riskin
- Book ID
- 106047531
- Publisher
- Springer Japan
- Year
- 2005
- Tongue
- English
- Weight
- 267 KB
- Volume
- 21
- Category
- Article
- ISSN
- 0911-0119
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๐ SIMILAR VOLUMES
We show that if \(G\) is a graph embedded on the torus \(S\) and each nonnullhomotopic closed curve on \(S\) intersects \(G\) at least \(r\) times, then \(G\) contains at least \(\left\lfloor\frac{3}{4} r\right\rfloor\) pairwise disjoint nonnullhomotopic circuits. The factor \(\frac{3}{4}\) is best
A construction is given for all the regular maps of type (3, 6} on the torus, with v vertices, v being any integer > 0. We also find bounds for the number of those maps, in particular for the case in which the maps contain "normal" Hamiltonian circuits. Using duality, the results may be applied for
## Let be the set of finite, simple and nondirected graphs being not embeddable into the torus. Furthermore let >4 be a partial order-relation and M, (r) the minimal basis of I'. In this paper we determine three graphs of M, (r) being embeddable into the projective plane and containing the subgrap