Small drawings of series-parallel graphs and other subclasses of planar graphs

Abstract

In this paper, we study small planar drawings of planar graphs. For arbitrary planar graphs, Θ(n2) is the established upper and lower bound on the worst-case area. It is a long-standing open problem for what graphs smaller area can be achieved, with results known only for trees and outer-planar graphs. We show here that series-parallel can be drawn in O(n 3/2) area, but 2-outer-planar graphs and planar graphs of proper pathwidth 3 require Ω(n2) area. © 2010 Springer-Verlag.