Non-aligned Drawings of Planar Graphs

A non-aligned drawing of a graph is a drawing where no two vertices are in the same row or column. Auber et al. showed that not all planar graphs have a non-aligned planar straight-line drawing in the n x n-grid. They also showed that such a drawing exists if up to n - 3 edges may have a bend. In this paper, we give algorithms for non-aligned planar drawings that improve on the results by Auber et al. In particular, we give such drawings in an n x n-grid with at most 2n-5/3 bends, and we study what grid-size can be achieved if we insist on having straight-line drawings.