In this paper we show that an outerplanar graph G with maximum degree at most 3 has a 2-D orthogonal drawing with no bends if and only if G contains no triangles. We also show that an outerplanar graph G with maximum degree at most 6 has a 3-D orthogonal drawing with no bends if and only if G contains no triangles.

A plane graph is a planar graph with a fixed embedding. In a no-bend orthogonal drawing of a plane graph, each vertex is drawn as a point and each edge is drawn as a single horizontal or vertical line segment. A planar graph is said to have a no-bend orthogonal drawing if at least one of its plane embeddings has a no-bend orthogonal drawing. In this paper we consider a class of planar graphs, called subdivisions of planar triconnected cubic graphs, and give a linear-time algorithm to examine whether such a planar graph G has a no-bend orthogonal drawing and to find one if G has.

Graph drawing addresses the problem of constructing geometric representation of information and finds applications in almost every branch of science and technology. Efficient algorithms are essential for automatic drawings of graphs, and hence a lot of research has been carried out in the last decade by many researchers over the world to develop efficient algorithms for drawing graphs. In this paper we survey the recent algorithmic results on various drawings of plane graphs: straight line drawing, convex drawing, orthogonal drawing, rectangular drawing and box-rectangular drawing.