Given a map M on a 2-manifold of genus ≥1, it is generally not known when is the map geometrically embeddable in R3. Sufficient conditions are given here in case M is a triangulation of the torus. Those conditions are based on Hamiltonian circuits of certain types and on other circuits in the given map. In the general case, sufficient conditions of a different nature are given. Also, the 2-dimensional skeletons of the cyclic 4-polytopes are studied, from the point of view of the 2-manifolds contained in them.
|Number of pages||28|
|State||Published - 1 Jan 1971|
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics