An optimal randomized parallel algorithm for finding connected components in a graph

We present a parallel randomized algorithm for finding the connected components of an undirected graph. Our algorithm takes T = O(log (n)) time and p = O(m+n/(log(n) processors, where m = number of edges and n = number of vertices. This algorithm ...

The subgraph of a 5-connected graph G induced by the set of degree 5 vertices is said to be the 5-subgraph of G. An edge of a 5-connected graph is said to be 5-contractible if the contraction of the edge results in a 5-connected graph. A 5-connected ...

An edge e of a k-connected graph G is said to be a removable edge if G@?e is still k-connected. A k-connected graph G is said to be a quasi (k+1)-connected if G has no nontrivial k-separator. The existence of removable edges of 3-connected and 4-...