Question: 1. In our previous lectures we studied complexity classes P and NP, as well as NP complete problems. The relations between those classes are shown

1. In our previous lectures we studied complexity classes P and NP, as well as NP complete problems. The relations between those classes are shown in the following diagram: NP Problems P Problems NP Complete Are there any problems that belong to the class NP, but lay outside both P and NP-complete (i.e. in the purple area of the diagram)? Can you name any such problem (or at least a problem that is suspected to belong to the purple area)? Find a reference to a paper or webpage with answers 2. Consider the following problem: Input: graph G, integer k Question: is it possible to partition vertices of G into k disjoint independent sets? Is this problem polynomial or NP-complete? Explain your

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