By a poly-line drawing of a graph G on n vertices we understand a drawing of G in the plane such that each edge is represented by a polygonal arc joining its two respective vertices. We call a turning point of a polygonal arc the bend. We consider the class of graphs that admit a poly-line drawing, in which each edge has at most one bend (resp. two bends) and any two edges can cross only at a right angle. It is shown that the number of edges of such graphs is at most O(n) (resp. O(n log 2 n)). This is a strengthening of a recent result of Didimo et al.
Arikushi et al. REF studied polyline RAC drawings in which each edge has at most one or two bends and proved that the number of edges is at most O(n) and O(n log 2 n), respectively.
Drawing Graphs with Orthogonal Crossings
arXiv: Combinatorics
Mathematics