An Algorithm for Determining Whether the Connectivity of a Graph is at Least k

The algorithm presented in this paper is for testing whether the connectivity of a large graph of $n$ vertices is at least $k$. First the case of undirected graphs is discussed, and then it is shown that a variation of this algorithm works for directed graphs. The number of steps the algorithm requires, in case $k > \sqrt{n}$, is bounded by $O(kn^{3})$.