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Given an undirected graph G = (V, E) on n vertices and m edges, we address the problem of maintaining a DFS tree when the graph is undergoing updates (insertion and deletion of vertices or edges). We present the following results for this problem. 1. Fault tolerant DFS tree: There exists a data structure of size˜O(m) 1 such that given any set F of failed… (More)

Depth first search (DFS) tree is a fundamental data structure for solving various problems in graphs. It is well known that it takes O(m + n) time to build a DFS tree for a given undirected graph G = (V, E) on n vertices and m edges. We address the problem of maintaining a DFS tree when the graph is undergoing updates (insertion and deletion of vertices or… (More)

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