The class of 2-interval graphs has been introduced for modelling scheduling and allocation problems, and more recently for specific bioinformatic problems. Some of those applications imply restrictions on the 2-interval graphs, and justify the introduction of a hierarchy of subclasses of 2-interval graphs that generalize line graphs: balanced 2-interval graphs, unit 2-interval graphs, and (x,x)...

For a fixed k, an oriented graph is k-transitive if it is acyclic and for every directed path p=u1→u2→...→uk+2 with k+2 vertices, p induces a clique if each of the two subpaths u1→u2→...→uk+1 and u2→...→uk+2 induces a clique. We describe an algorithm to find a maximum weight clique in a k-transitive graph. Consider a hereditary family G of graphs. A graph H(V,E) is called G-k-mixed if its edge ...

In a recent paper, we introduced the simultaneous representation problem (defined for any graph class C) and studied the problem for chordal, comparability and permutation graphs. For interval graphs, the problem is defined as follows. Two interval graphs G1 and G2, sharing some vertices I (and the corresponding induced edges), are said to be “simultaneous interval graphs” if there exist interv...

We present an algorithm that produces a schedule of transmissions to achieve gossiping in a system where nodes are equipped with radio transceivers; diierent nodes have transceivers with diierent ranges. We assume that all the nodes are placed on a line and that all communication occurs in one dimension. Finally, unlike traditional system models for gossiping, we assume that all nodes within ra...

Interval graphs arose in the nineteen fifties and have become a staple of graph theory, both for their appealing applications and for their rich mathematical structure yielding elegant characterizations and efficient algorithms. Recently, interval graphs have naturally appeared in the context of constraint satisfaction problems. Progress in understanding what structures make CSP’s tractable sug...

We define the Cartesian product, composition, union and join on interval-valued fuzzy graphs and investigate some of their properties. We also introduce the notion of interval-valued fuzzy complete graphs and present some properties of self complementary and self weak complementary interval-valued fuzzy complete graphs.

In this paper we extend the work of Rautenbach and Szwarcfiter [8] by giving a structural characterization of graphs that can be represented by the intersection of unit intervals that may or may not contain their endpoints. A characterization was proved independently by Joos in [6], however our approach provides an algorithm that produces such a representation, as well as a forbidden graph char...

A Shiftable Interval Graph (SIG) is defined by a set of intervals and a set of windows associated with the intervals. Each interval does not have a fixed position, but it is allowed to move, provided that it remains completely contained into its window. Once a position has been fixed for all the intervals, the graph becomes an usual interval graph. In this paper we address the problem of findin...