Pathwidth and small-height drawings of 2-connected outer-planar graphs

Abstract

In this paper, we study planar drawings of 2-connected outer-planar graphs. In an earlier paper we showed that every such graph has a visibility representation with height O(log n). In this paper, we show that with a different construction, the height is 4pw(G)-3, where pw(G) denotes the pathwidth of graph G. Since for any planar graph G, any planar drawing has height >=pw(G), this is a 4-approximation algorithm for the height. We also show that our visibility representations can be converted into straight-line drawings of the same height.