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...

In this note, we study a constrained independent set problem for matroids and certain generalizations. The basic problem can be regarded as an ordered version of the matroid parity problem. By a reduction of this problem to matroid intersection, we prove a min-max formula. Studying the weighted case and a delta-matroid generalization, we prove that some of them are not more complex than matroid...

We analyze the component evolution in inhomogeneous random intersection graphs when the average degree is close to 1. As the average degree increases, the size of the largest component in the random intersection graph goes through a phase transition. We give bounds on the size of the largest components before and after this transition. We also prove that the largest component after the transiti...

A package for the Sage computer algebra system is developed for checking feasibility of a given intersection array for a distance-regular graph. We use this tool to show that there is no distance-regular graph with intersection array {(2r + 1)(4r + 1)(4t− 1), 8r(4rt− r + 2t), (r + t)(4r + 1); 1, (r + t)(4r + 1), 4r(2r + 1)(4t− 1)} (r, t ≥ 1), {135,128,16; 1,16,120}, {234,165,12; 1,30,198} or {5...

We focus on the elliptic genera of level N at cusps a congruence subgroup for any complete intersection. Writing first Chern class intersection as product an integral coefficient c1 and generator 2nd cohomology group, we mainly discuss values in cases >, =, or < 0. In particular, about Todd genus, Â-genus, Ak-genus can be derived from N.

The paper presents a new robust method for finding points of intersection of line segments in the plane. In this method the subdivision of the plane based on the Delaunay triangulation plays the main role. First, the Delaunay triangulation spanning the end points of line segments is constructed. Next, for line segments that are not realized by Delaunay edges, midpoints are inserted recursively ...

In CAD/CAM modeling, objects are represented using the Boundary Representation (ANSI Brep) model. Detection of possible intersection between objects can be based on the objects’ boundaries (i.e., triangulated surfaces), and computed using triangle-triangle intersection. Usually only a cross intersection algorithm is needed; however, it is beneficial to have a single robust and fast intersection...

Outerstring graphs are the intersection graphs of curves that lie inside a disk such that each curve intersects the boundary of the disk. Outerstring graphs are among the most general classes of intersection graphs studied. To date, no polynomial time algorithm is known for any of the classical graph optimization problems on outerstring graphs; in fact, most are NP-hard. It is known that there ...

A graph is clique-Helly if any family of mutually intersecting (maximal) cliques has non-empty intersection, and it is hereditary clique-Helly (abbreviated HCH) if its induced subgraphs are clique-Helly. The clique graph of a graph G is the intersection graph of its cliques, and G is self-clique if it is connected and isomorphic to its clique graph. We show that every HCH graph is an induced su...