An undirected graph component can be represented as a Tree and a set of back edges. Thinking about a graph in this representation simplifies a large number of graph problems and algorithms.
0:00 Intro and applications
1:05 The DFS tree representation
1:37 Lets create the DFS Tree
4:35 Graph = Tree + Back Edges
5:00 Find if Graph is cyclic
5:38 What is an articulation point?
6:08 Marking levels in the tree
6:28 Algorithm for articulation points
7:45 Summary
Reference blog: https://codeforces.com/blog/entry/68138
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