Publication Title
Discrete Mathematics
Volume
131
Publication Date
1994
Document Type
Article
Issue
1
First and Last Page
211-219
Abstract
In this paper we show that if attention is restricted to polyhedral embeddings of graphs, no theorem analogous to the Duke interpolation theorem for 2-cell embeddings is true. We also give two interesting classes of graphs: (i) a class in which the members have polyhedral embeddings in the torus and also in orientable manifolds of arbitrarily high genus, (ii) and another in which the members have polyhedral embeddings in the projective plane and also in orientable and nonorientable manifolds of arbitrarily low Euler characteristic.
Recommended Citation
On the noninterpolation of polyhedral maps. (1994). Discrete Mathematics, 131(1), 211-219. https://doi.org/10.1016/0012-365X(94)90386-7