A Simple Linear Time Algorithm for Proper Box Rectangular Drawings of Plane Graphs

In this paper we introduce a new drawing style of a plane graph G, called proper box rectangular (PBR) drawing. It is deened to be a drawing of G such that every vertex is drawn as a rectangle, called a box, each edge is drawn as either a horizontal or a vertical line segment, and each face is drawn as a rectangle. We establish necessary and suucient conditions for G to have a PBR drawing. We also give a simple linear time algorithm for nding such drawings. The PBR drawing is closely related to the box rectangular (BR) drawing deened by Rahman, Nakano and Nishizeki 17]. Our method can be adapted to provide a new simpler algorithm for solving the BR drawing problem.