Straight-line monotone grid drawings of series–parallel graphs

A monotone drawing of a planar graph G is a planar straight-line drawing of G where a monotone path exists between every pair of vertices of G in some direction. Recently monotone drawings of graphs have been discovered as a new standard for visualizing graphs. In this paper we study monotone drawings of series–parallel graphs in a variable embedding setting. We show that a series–parallel graph of n vertices has a straight-line planar monotone drawing on a grid of size O(n) × O(n2) and such a drawing can be found in linear time.