We adapt the classical 3-decomposition of any 2-connected graph to the case of simple graphs (no loops or multiple edges). By analogy with the block-cutpoint tree of a connected graph, we deduce from this decomposition a bicolored tree tc(g) associated with any 2-connected graph g, whose white vertices are the 3-components of g (3-connected components or polygons) and whose black vertices are b...

A directed graph G (V, E) is strongly connected if and only if, for any pair of vertices X and Y from V, there exists a path from X to Y and a path from Y to X. In Computer Science, the partition of a graph in strongly connected components is represented by the partition of all vertices from the graph, so that for any two vertices, X and Y, from the same partition, there exists a path from X to...

We present a new CREW PRAM algorithm for nding connected components. For a graphG with n vertices andm edges, algorithmA0 requires at mostO(logn) parallel steps and performsO((n+m) logn) work in the worst case. The advantage our algorithm has over others in the literature is that it can be adapted to a 2-D mesh-connected communication model in which all CREW operations are replaced byO(logn) pa...