Monotone Drawings of k-Inner Planar Graphs

08/21/2018

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by   Anargyros Oikonomou, et al.

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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 × 2(k+1)n grid. In the special case of an outerplanar graph, we can produce a planar monotone drawing on a n × n grid, improving previously known results.