The Problem of Outer-Embeddings in Pseudosurfaces

Abstract

Many results about outer-embeddings (graphs having all their vertices in the same face) have been obtained recently in topological graph theory in recent times. In this paper, we deal with some difficulties appearing in the study of such embeddings. Particularly, we propose several problems concerning outer-embeddings in pseudosurfaces and we prove that two of them are NP-complete.

We also describe some properties about lists of forbidden minors for outer-embeddings in certain kinds of pseudosurfaces.