Max weighted independent set returns a set of nodes that form the maximum weighted independent set. K-independent set returns yes/no if the graph has a independent set of size k. How would you go about proving this?
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Maximum weighted independent set is an optimization problem. NP-hardness is a category of decision problems. So the first step would be formulating the decision problem corresponding to your optimization problem. Once you do that, the reduction should become obvious. – Yuval Filmus Jun 12 '18 at 06:42
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@YuvalFilmus It's entirely standard to describe a function problem as NP-hard if an oracle for it would let you decide NP-complete problems in polytime. – David Richerby Jun 12 '18 at 11:30
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@YuvalFilmus thank you! I understand now – notorious Jun 12 '18 at 13:13