Monotone Grid Drawings of Planar Graphs

Amonotone drawing of a planar graph G is a planar straightline drawing of G where a monotone path exists between every pair of vertices of G in some direction. Recently monotone drawings of planar graphs have been proposed as a new standard for visualizing graphs. A monotone drawing of a planar graph is a monotone grid drawing if every vertex in the drawing is drawn on a grid point. In this paper we study monotone grid drawings of planar graphs in a variable embedding setting. We show that every connected planar graph of n vertices has a monotone grid drawing on a grid of size O(n) × O(n), and such a drawing can be found in O(n) time.