given an undirected graph, you have to remove some nodes to maximize the number of connected components.
when removing a node, you have to remove all its edges.
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Auto comment: topic has been updated by TuHoangAnh (previous revision, new revision, compare).
It's just the size of maximum independent set.
Proof: If the optimal set of remaining vertices doesn't form an independent set, simply take one vertex from each of the components.