Interval graphs have engaged the interest of researchers for over twenty-five years. The scope of current research in this area now extends to the mathematical and algorithmic properties of interval graphs, their generalizations, and graph parameters motivated by them. One main reason for this increasing interest is that many real-world applications involve solving problems on graphs which are ...

We study a variant of intersection representations with unit balls: unit disks in the plane and unit intervals on the line. Given a planar graph and a bipartition of the edges of the graph into near and far edges, the goal is to represent the vertices of the graph by unit-size balls so that the balls for two adjacent vertices intersect if and only if the corresponding edge is near. We consider ...

We study the online matroid intersection problem, which is related to the well-studied online bipartite matching problem in the vertex arrival model. For two matroids M1 and M2 defined on the same ground set E, the problem is to design an algorithm that constructs a large common independent set in an online fashion. The algorithm is presented with the ground set elements one-by-one in a uniform...

An innovative treatment for congested urban road networks is the split intersection. Here, a two-way–two-way traffic light-controlled intersection transformed into two lighter intersections. By reducing conflict points and improving travel time, it facilitates smoother flow with less driver delay. We propose visible light communication system based on Vehicle-to-Vehicle (V2V), Vehicle-to-Infras...

Progressive meshes are an established tool for triangle mesh simplification. By suitably adapting the simplification process, progressive hulls can be generated which enclose the original mesh in gradually simpler, nested meshes. We couple progressive hulls with a selective refinement framework and use them in applications involving intersection queries on the mesh. We demonstrate that selectiv...

Let A = fC 1 ; C 2 ; : : : ; C n g be an arrangement of Jordan curves in the plane lying in general position, i.e., every curve properly intersects at least one other curve, no two curves touch each other and no three meet at a common intersection point. The Jordancurve arrangement graph of A has as its vertices the intersection points of the curves in A, and two vertices are connected by an ed...

Let T = (V,A) be a directed tree. Given a collection P of dipaths on T , we can look at the arc-intersection graph I(P, T ) whose vertex set is P and where two vertices are connected by an edge if the corresponding dipaths share a common arc. Monma and Wei, who started their study in a seminal paper on intersection graphs of paths on a tree, called them DE graphs (for directed edge path graphs)...

A graph G = (V, E) is a pairwise compatibility graph (PCG) if there exists an edgeweighted tree T and two non-negative real numbers dmin and dmax such that each leaf u of T is a node of V and there is an edge (u, v) ∈ E if and only if dmin ≤ dT (u, v) ≤ dmax where dT (u, v) is the sum of weights of the edges on the unique path from u to v in T . The main issue on these graphs consists in charac...

Let ~ be a family of sets. The intersection graph of ~ is obtained by representing each set in N' by a vertex and connecting two vertices by an edge if and only if their corresponding sets intersect. Of primary interest are those classes of intersection graphs of families of sets having some specific topological or other structure. The "grandfather" of all intersection graphs is the class of in...