Abstract
A shape visibility representation displays a graph so that each vertex is represented by an orthogonal polygon of a particular shape and for each edge there is a horizontal or vertical line of sight of width ϵ>0 between the polygons assigned to its endvertices. Special shapes are rectangles, L, T, E, and H-shapes, and caterpillars. A graph is 1-planar if there is a drawing in the plane such that each edge is crossed at most once and is IC-planar if in addition no two crossed edges share a vertex.We show that every IC-planar graph has a flat rectangle visibility representation, in which each rectangle has height ϵ, and that every 1-planar graph has a T-shape visibility representation. The representations use quadratic area and can be computed in linear time from a given embedding.
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call