Improved algorithms for graph four-connectivity

We present a new algorithm based on ear decomposition for testing vertex four-connectivity and for finding all separating triplets in a triconnected graph. The sequential implementation of our algorithm runs in O(n2) time and the parallel implementation runs in O(logn) time using O(n2) processors on a CRCW PRAM, where n is the number of vertices in the graph. This improves previous bounds for the problem for both the sequential and parallel cases. The sequential algorithm is optimal if the input is specified in adjacency matrix form, or if the input graph is dense.