A chordal graph is the intersection graph of a family of subtrees of a tree, or, equivalently, it is the (edge-)intersection graph of leaf-generated subtrees of a full binary tree. In this paper, a generalization of chordal graphs from this viewpoint is studied: a graph G=(V; E) is representable if there is a family of subtrees {Sv}v∈V of a binary tree, such that uv ∈ E if and only if |Su ∩ Sv|...

Let P be a collection of nontrivial simple paths in a tree T . The edge intersection graph of P , denoted by EPT (P), has vertex set that corresponds to the members of P , and two vertices are joined by an edge if the corresponding members of P share a common edge in T . An undirected graph G is called an edge intersection graph of paths in a tree, if G = EPT (P) for some P and T . The EPT grap...

In this paper we begin the classification completed in [12] of all partial linear spaces n , graphs F, and groups G which satisfy one of the following: I. II = (0>, ££) is a connected partial linear space of order 2 in which every pair of intersecting lines lies in a subspace isomorphic to the dual of an affine plane of order 2; II. F is a connected graph such that, for each vertex x of F, the ...

A disk graph is the intersection graph of disks in the plane, a unit disk graph is the intersection graph of same radius disks in the plane, and a segment graph is an intersection graph of line segments in the plane. Every disk graph can be realized by disks with centers on the integer grid and with integer radii; and similarly every unit disk graph can be realized by disks with centers on the ...

We extend the notion of a minor from matroids to simplicial complexes. We show that the class of matroids, as well as the class of independence complexes, is characterized by a single forbidden minor. Inspired by a recent result of Aharoni and Berger, we investigate possible ways to extend the matroid intersection theorem to simplicial complexes.

In this paper, we show that for any independence system, the problem of finding a persistency partition of the ground set and that of finding a maximum weight independent set are polynomially equivalent.

We present a systematic study of the expected complexity of the intersection of geometric objects. We first study the expected size of the intersection between a random Voronoi diagram and a generic geometric object that consists of a finite collection of line segments in the plane. Using this result, we explore the intersection complexity of a random Voronoi diagram with the following target o...

We consider a generalization of edge intersection graphs of paths in a tree. Let P be a collection of nontrivial simple paths in a tree T . We define the k-edge (k 1) intersection graph k(P), whose vertices correspond to the members of P, and two vertices are joined by an edge if the corresponding members ofP share k edges in T . An undirected graphG is called a k-edge intersection graph of pat...

We consider a generalization of edge intersection graphs of paths in a tree. Let P be a collection of nontrivial simple paths in a tree T . We define the k-edge (k ≥ 1) intersection graph Γk(P), whose vertices correspond to the members of P, and two vertices are joined by an edge if the corresponding members of P share k edges in T . An undirected graph G is called a k-edge intersection graph o...

In this paper, we consider the intersection graph IΓ(Zn) of gamma sets in the total graph on Zn. We characterize the values of n for which IΓ(Zn) is complete, bipartite, cycle, chordal and planar. Further, we prove that IΓ(Zn) is an Eulerian, Hamiltonian and as well as a pancyclic graph. Also we obtain the value of the independent number, the clique number, the chromatic number, the connectivit...