Monotone Drawings Of K-Inner Planar Graphs

A k-inner planar graph is a planar graph that has a plane drawing with at most k internal vertices, i.e., vertices that do not lie on the boundary of the outer face of its drawing. An outerplanar graph is a 0-inner planar graph. In this paper, we show how to construct a monotone drawing of a k-inner planar graph on a 2(k + 1)n x 2(k + 1)n grid. In the special case of an outerplanar graph, we can produce a planar monotone drawing on a n x n grid, improving the results in [2,11].