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Problem : You are given a connected graph with N nodes and M edges, graph does not contain multiple edges and self loops. An independent set of nodes is the set in which no two nodes are connected to each other. You need to find the largest independent set.
Constraints : 3 <= N <= 1e5 and (N — 1) <= M <= 2e5
It is NP-hard problem in general.
any Proof for why is it NP — hard ?
page 12 of this
NP hardness also noted in "Independent set (graph theory)" wikipedia article.