Improved Lower Bounds on the Area Requirements of Series-Parallel Graphs

We show that there exist series-parallel graphs requiring Ω(n2 √ ) area in any straight-line or poly-line grid drawing. Such a result is achieved in two steps. First, we show that, in any straight-line or poly-line drawing of K2,n, one side of the bounding box has length Ω(n), thus answering two questions posed by Biedl et al. Second, we show a family of series-parallel graphs requiring Ω(2 √ ) width and Ω(2 √ ) height in any straight-line or poly-line grid drawing. Combining the two results, the Ω(n2 √ ) area lower bound is achieved.