In this paper we introduce unit bar k-visibility graphs, which are bar kvisibility graphs in which every bar has unit length. We show that almost all families of unit bar k-visibility graphs and unit bar k-visibility graphs are incomparable under set inclusion. In addition, we establish the largest complete graph that is a unit bar k-visibility graph. As well, we present a family of hyperbox vi...

hyperactivity disorder (ADHD) Ainara Mira-Iglesias; J. Alberto Conejero; Esperanza Navarro-Pardo Fundación para el Fomento de la Investigación Sanitaria y Biomédica de la Comunidad Valenciana (FISABIO), Valencia, Spain Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Spain Departamento de Psicoloǵıa Evolutiva y de la Educación, Universitat de València,...

A visibility representation of a graph G is an assignment of the vertices of G to geometric objects such that vertices are adjacent if and only if their corresponding objects are “visible” each other, that is, there is an uninterrupted channel, usually axis-aligned, between them. Depending on the objects and definition of visibility used, not all graphs are visibility graphs. In such situations...

Given an arbitrary polygon P with holes, we construct a polytopal complex analogous to the associahedron based on convex diagonalizations of P . This polytopal complex is shown to be contractible, and a geometric realization is provided based on the theory of secondary polytopes. We then reformulate a combinatorial deformation theory and present an open problem based on visibility which is a cl...

In this paper we give tight lower bounds on the size of the visibility graph, the contracted visibility graph, and the bar-visibility graph of n disjoint line segments in the plane, according to their vertex-connectivity.

We study polar visibility graphs, graphs whose vertices can be represented by arcs of concentric circles with adjacency determined by radial visibility including visibility through the origin. These graphs are more general than the well-studied bar-visibility graphs and are characterized here, when arcs are proper subsets of circles, as the graphs that embed on the plane with all but at most on...

Let P be a finite set of points in the plane and S a set of non-crossing line segments with endpoints in P . The visibility graph of P with respect to S, denoted Vis(P, S), has vertex set P and an edge for each pair of vertices u, v in P for which no line segment of S properly intersects uv. We show that the constrained half-θ6-graph (which is identical to the constrained Delaunay graph whose e...

Everett et al. [EHN96, EHN97] introduced several varieties of stabbing information for the lines determined by pairs of vertices of a simple polygon P , and established their relationships to vertex visibility and other combinatorial data. In the same spirit, we define the “zero-parity (ZP) stabbing information” to be a natural weakening of their “weak stabbing information,” retaining only the ...

The subject of this thesis is the problem of computing the visibility graph of m points P within a polygon Q. The vertices of the visibility graph are the points of P and the edges of the graph are the pairs of points in P×P , where the line between them is fully contained inside Q. Known algorithms by Ben-Moshe et al. are presented for computing the visibility graph of a simple polygon, the vi...

In this paper we present a very simple proof of the following result due to Abello et al [5], concerning the visibility graphs of simple polygons. The result says that the visibility graph of any simple nondegenerate polygon is isomorphic to the visibility graph of some simple staircase polygon. As a result of the above proof we also give an O(n log n) time algorithm for the following problem: ...