T. U. Berlin
Combinatorics of Orthogonal Surfaces
Orthogonal surfaces allow a very natural approach to Schnyder woods on planar graphs which continue to find new applications in graph drawing, enumeration and in dimension theory of orders. These connections motivated the independent study of orthogonal surfaces. We give an overview on recent results and problems in this area. This includes a slick proof of the Brightwell-Trotter Theorem about the order dimension 3-polytopes, new bounds for the number of edges of some classes of box-graphs and the notion of a cp-order of an orthogonal surface which seems to be crucial for the study of orthogonal surfaces in higher dimensions.