GATE | GATE-CS-2005 | Question 58

Consider the following two problems on undirected graphs

α : Given G(V, E), does G have an independent set of size | V | - 4?
β : Given G(V, E), does G have an independent set of size 5? 

Which one of the following is TRUE?

(A) α is in P and β is NP-complete
(B) α is NP-complete and β is in P
(C) Both α and β are NP-complete
(D) Both α and β are in P


Answer: (C)

Explanation: Graph independent set decision problem is NP Complete.

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