Path-Width and Three-Dimensional Straight-Line Grid Drawings of Graphs

We prove that every n-vertex graph with path-width pw(G) a three-dimensional straight-line drawing with O(pw(G) u-g Thu graphs with bou58j path-width volu7 is O(n), follows that graphs with bou602 tree-width,su series-parallel graphs, the voluV O(n log 2 n). better bouV than ) pre- viouXj known drawings series-parallel graphs. For planar graphs obtain three-dimensional drawings with O(n ) voluX and aspect ratio, whereas constru6V85g with O(n 2 ) volu8 have #(n) aspect ratio