We give a simple argument showing that the number of edges in the intersection graph G of a family of n sets in the plane with a linear unioncomplexity is O(ω(G)n). In particular, we prove χ(G) 6 col(G) < 19ω(G) for intersection graph G of a family of pseudo-discs, which improves a previous

Let R be a ring with unity and I(R) be the set of all non-trivial left ideals of R. The intersection graph of ideals of R, denoted by G(R), is a graph with the vertex set I(R) and two distinct vertices I and J are adjacent if and only if I ∩ J 6= 0. In this paper, we study some connections between the graph-theoretic properties of this graph and some algebraic properties of rings. We characteri...

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 investigate which chordal graphs have a representation as intersection graphs of pseudosegments. For positive we have a construction which shows that all chordal graphs that can be represented as intersection graph of subpaths on a tree are pseudosegment intersection graphs. We then study the limits of representability. We describe a family of intersection graphs of substars of a star which ...

An interval graph is the intersection graph of a finite set of intervals on a line and a circular-arc graph is the intersection graph of a finite set of arcs on a circle. While a forbidden induced subgraph characterization of interval graphs was found fifty years ago, finding an analogous characterization for circular-arc graphs is a long-standing open problem. In this work, we study the inters...

We combine the known notion of the edge intersection graphs of paths in a tree with a VLSI grid layout model to introduce the edge intersection graphs of paths on a grid. Let P be a collection of nontrivial simple paths on a grid G. We define the edge intersection graph EPG(P) of P to have vertices which correspond to the members of P, such that two vertices are adjacent in EPG(P) if the corres...