Incremental Algorithm for Maintaining a DFS Tree for Undirected Graphs

Depth First Search (DFS) tree is a fundamental data structure for graphs used in solving various algorithmic problems. However, very few results are known for maintaining DFS tree in a dynamic environment–insertion or deletion of edges. We present the first algorithm for maintaining a DFS tree for an undirected graph under insertion of edges. For processing any arbitrary online sequence of edge insertions, this algorithm takes total $O(n^2)$ time.