A linear time algorithm for triconnectivity augmentation

The problem of finding the smallest set of edges whose addition triconnects an undirected graph is considered. This is a fundamental graph-theoretic problem that has applications in designing reliable networks and fault-tolerant computing. A linear time sequential algorithm is given for the problem. This is a substantial improvement over the best previous algorithm for this problem, which runs in O(n(n+m)²) time on a graph with n vertices and m edges