# Orthogonal Drawings of Plane Graphs without Bends

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## Abstract

In an orthogonal drawing of a plane graph *G* each vertex is drawn as a point and each edge is drawn as a sequence of vertical and horizontal line segments. A point at which the drawing of an edge changes its direction is called a bend. 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.

### Keywords

Graph Algorithm Graph Drawing Orthogonal Drawing Bend Download
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### References

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© Springer-Verlag Berlin Heidelberg 2002