(1) If Y ∈ NP-COMPLETE, X ∈ NP, and X ≤P Y, then X in NP-COMPLETE.
(2) Is it possible that P = NP and NP = EXP?
(3) Is it possible that both NP = PSPACE?
(4) For some NP-hard problems, a constant approximation solution is not possible.
(5) For some NP-hard problems, they can be approximated arbitrarily close to the optimum.
(6) The relationship between maximum independent set and minimum vertex cover is like the relationship between maximum flow and minimum cut.
(7) In a tournament, there always exists one or more Hamiltonian paths. In such a path, each player always beats its immediate successor.
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