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MOTIVATION Networks have been used to model many real-world phenomena to better understand the phenomena and to guide experiments in order to predict their behavior. Since incorrect models lead to incorrect predictions, it is vital to have as accurate a model as possible. As a result, new techniques and models for analyzing and modeling real-world networks… (More)
A tree t-spanner T of a graph G is a spanning tree in which the distance between every pair of vertices is at most t times their distance in G. This notion is motivated by applications in communication networks, distributed systems, and network design. This paper studies graph theoretic, algorithmic and complexity issues about tree spanners. It is shown… (More)
An independent set of three vertices such that each pair is joined by a path that avoids the neighborhood of the third is called an asteroidal triple. A graph is asteroidal triple-free (AT-free) if it contains no asteroidal triples. The motivation for this investigation was provided, in part, by the fact that the AT-free graphs provide a common… (More)
We present a linear time algorithm for unit interval graph recognition. The algorithm is simple and based on Breadth-First Search. It is also direct | it does not rst recognize the graph as an interval graph. Given a graph G, the algorithm produces an ordering of the vertices of the graph whenever G is a unit interval graph. This order corresponds to the… (More)
We present a simple linear time algorithm for unit interval graph recognition. This algorithm uses 3 LBFS sweeps and then a very simple test to determine if the given graph is a unit interval graph. It is argued that this algorithm is the most easily implementable unit interval graph recognition algorithm known.