Publication Title
Discrete Mathematics
Volume
234
Publication Date
2001
Document Type
Article
First and Last Page
77-88
Abstract
We show that toroidal polyhedral maps with four or more disjoint homotopic noncontractiblecircuits are not embeddable on the projective plane and that toroidal polyhedral maps with -veor more disjoint homotopic noncontractible circuits are not embeddable on the Klein bottle. Wealso show that the Klein bottle crossing numbers ofCm×Cn(m6n) form=3;4;5;6 are 1,2,4,and 6, respectively, and give upper bounds for all other values ofn. These crossing numbersdispla yat ypical behavior in that the value depends onl yonminstead of on bothmandnas isthe case for the plane and projective plane.
Recommended Citation
Riskin, A. (2001). On the nonembeddability and crossing numbers of some toroidal graphs on the Klein bottle. Discrete Mathematics, 234(1), 77–88. 10.1016/S0012-365X(00)00193-X