Projective plane embeddings of polyhedral pinched maps (Q1318818)

A map (or embedding of a graph in a compact 2-manifold) is called closed 2-cell provided that the closure of each region is a 2-cell. A polyhedral map on the pinched torus is called a pinched polyhedral map, and the projective plane is denoted by \(\Pi\). The first part deals with two cases in which a pinched polyhedral map is not \(\Pi\)-embeddable. The main result states that a \(\Pi\)-embedding of a pinched polyhedral map must be closed 2-cell, but cannot be polyhedral.