  The edge-length ratio of a straight-line drawing of a graph is the ratio
between the lengths of the longest and of the shortest edge in the drawing. The
planar edge-length ratio of a planar graph is the minimum edge-length ratio of
any planar straight-line drawing of the graph.
  In this paper, we study the planar edge-length ratio of planar graphs. We
prove that there exist $n$-vertex planar graphs whose planar edge-length ratio
is in $\Omega(n)$; this bound is tight. We also prove upper bounds on the
planar edge-length ratio of several families of planar graphs, including
series-parallel graphs and bipartite planar graphs.
