Drawing HV-Restricted Planar Graphs

A strict orthogonal drawing of a graph G = (V,E) in R is a drawing of G such that each vertex is mapped to a distinct point and each edge is mapped to a horizontal or vertical line segment. A graph G is HV -restricted if each of its edges is assigned a horizontal or vertical orientation. A strict orthogonal drawing of an HV -restricted graph G is good if it is planar and respects the edge orientations of G. In this paper we give a polynomial-time algorithm to check whether a given HV -restricted plane graph (i.e., a planar graph with a fixed combinatorial embedding) admits a good orthogonal drawing preserving the input embedding, which settles an open question posed by Maňuch, Patterson, Poon and Thachuk (GD 2010). We then examine HV -restricted planar graphs (i.e., when the embedding is not fixed). Here we completely characterize the 2-connected maximum-degree-three HV -restricted outerplanar graphs that admit good orthogonal drawings.