Orthogonal Drawings of Plane Graphs without Bends

In an orthogonal drawing of a plane graph each vertex is drawn as a point and each edge is drawn as a sequence of vertical and horizontal line segments. A bend is a point at which the drawing of an edge changes its direction. Every plane graph of the maximum degree at most four has an orthogonal drawing, but may need bends. A simple necessary and sufficient condition has not been known for a plane graph to have an orthogonal drawing without bends. In this paper we obtain a necessary and sufficient condition for a plane graph G of the maximum degree three to have an orthogonal drawing without bends. We also give a linear-time algorithm to find such a drawing of G if it exists. Communicated by: P. Mutzel and M. J¨unger; submitted May 2002; revised November 2002. Part of this work was done while the first and the third authors were in Bangladesh University of Engineering and Technology (BUET). This work is supported by the grants of Japan Society for the Promotion of Science (JSPS). ...

• Type: Conference
• Year: 2001
• Where: GD
• Authors: Md. Saidur Rahman, Mahmuda Naznin, Takao Nishizeki
• Keywords: Computer Graphics, GD 2001, Maximum Degree, Orthogonal Drawing, Plane Graph