Non-aligned Drawings of Planar Graphs

Abstract

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 $n\times n$-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 on an $n\times n$-grid with at most $\frac{2n-5}{3}$ bends, and we study what grid-size can be achieved if we insist on having straight-line drawings.