L-visibility drawings of IC-planar graphs

•We study visibility representations of IC-planar graphs.•We show that every IC-planar graph has an L-visibility drawing in quadratic area which can be computed in linear time.•We prove that every IC-planar graph has a RAC drawing in quadratic area with at most two bends per edge.

An IC-plane graph is a topological graph where every edge is crossed at most once and no two crossed edges share a vertex. We show that every IC-plane graph has a visibility drawing where every vertex is of the form {,,,}{,,,}, and every edge is either a horizontal or vertical segment. As a byproduct of our drawing technique, we prove that every IC-plane graph has a RAC drawing in quadratic area with at most two bends per edge.