We obtain the rst NC algorithm for the low-diameter graph decomposition problem on arbitrary graphs. Our algorithm runs in O(log5 (n)) time, and uses O(n2) processors.
We introduce an energy model whose minimum energy drawings reveal the clusters of the drawn graph. Here a cluster is a set of nodes with many internal edges and few edges to nodes ...
Krishnamoorthy, Thulasiraman and Swamy [Minimum order graphs with specified diameter, connectivity and regularity, Networks 19 (1989) 25–46] showed that a δ-regular graph with...
Let G = (V, E) be an weighted undirected graph on n vertices and m edges, and let dG be its shortest path metric. We present two simple deterministic algorithms for approximating ...
A spanning tree T in a finite planar connected graph G determines a dual spanning tree T in the dual graph G such that T and T do not intersect. We show that it is not always poss...