Visibility Representations of Four-Connected Plane Graphs with Near Optimal Heights

Width-Optimal Visibility Representations of Plane Graphs

Simultaneous Visibility Representations of Plane st-graphs Using L-shapes

Let 〈Gr, Gb〉 be a pair of plane st-graphs with the same vertex set V . A simultaneous visibility representation with L-shapes of 〈Gr, Gb〉 is a pair of bar visibility representations 〈Γr, Γb〉 such that, for every vertex v ∈ V , Γr(v) and Γb(v) are a horizontal and a vertical segment, which share an end-point. In other words, every vertex is drawn as an L-shape, every edge of Gr is a vertical vis...

Graphs with Plane Outside-Obstacle Representations

An obstacle representation of a graph consists of a set of polygonal obstacles and a distinct point for each vertex such that two points see each other if and only if the corresponding vertices are adjacent. Obstacle representations are a recent generalization of classical polygon–vertex visibility graphs, for which the characterization and recognition problems are long-standing open questions....

Rectangle-Visibility Representations of Bipartite Graphs

The paper considers representations of bipartite graphs as rectangle-visibility graphs, Le., graphs whose vertices are rectangles in the plane, with adjacency detenmned by horizontal and vertical visibility.1t is shown that, for p ~ q, Kp,q has a representation with no rectangles having collinear sides if and only if p ~ 2 or p = 3 and q ~ 4. More generally, it is shown that Kp;q is a rectangle...

Representations of Graphs on a Cylinder

A complete characterization of the class of graphs that admit a cylindric visibility representation is presented, where vertices are represented by intervals parallel to the axis ofthe cylinder and the edges correspond to pairs of visible intervals. Moreover, linear time algorithms are given for testing the existence of and constructing such a representation. Important applications of cylindric...