An Algorithm For 1-bend Embeddings Of Plane Graphs In The Two-dimensional Grid

In this paper we characterize the class of plane graphs that can be embedded on the two-dimensional grid with at most one bend on each edge. In addition, we provide an algorithm that either detects a forbidden configuration or generates an embedding with at most one bend on each edge. © 2003 Elsevier B.V. All rights reserved.1411-3225241Liu, Y., (1995) Embeddability in Graphs, , Amsterdam: Kluwer Academic PublishersLiu, Y., Morgana, A., Simeone, B., General theoretical results on rectilinear embeddability of graphs (1991) Acta Math. Appl. Sinica, 7, pp. 187-192Liu, Y., Morgana, A., Simeone, B., A linear algorithm for 2-bend embeddings of planar graphs in the two-dimensional grid (1998) Discrete Appl. Math., 81, pp. 69-91Tarjan, R.E., Depth-first search and linear graph algorithms (1972) SIAM J. Comput., 1, pp. 146-16