Cycle or path polytopes are the convex hulls of the incidence vectors of (directed) cycles or paths in graphs (digraphs), respectively. By admitting not all cardinalities of paths or cycles ($=$ number of edges), we obtain cardinality restricted path or cycle polytopes.

The subject of this project is to investigate the coherence between different cycle and path polytopes. The aim is to gain more insight into these objects and to develop methods for transmission of the associated inequalities. From this we expect to gain advances by the solution of problems in connection with telecommunication and traffic networks such as line planning in public transport.