|Title:|| RECTILINEAR PLANAR DRAWINGS WITH FEW BENDS IN EACH EDGE.
|Authors:|| S. Even and G. Granot
For a 4-planar graph, a linear time algorithm is described to construct a planar drawing on the rectilinear grid, with at most 3 bends in each edge. The drawings found by this algorithm, for 3-planar graphs, have at most 2 bends in each edge. The drawings have O(n^2) area, a global number of O(n) bends and edges of length O(n). We also show a 4-planar graph that has no rectilinear planar drawing with at most 2 bends in each edge, and a 3-planar graph that has no rectilinear planar drawing with at most 1 bend in each edge.
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