It is NP-complete to determine whether an arbitrary graph has chromatic number k, where k >= 3. However, determining whether an arbitrary graph has chromatic number 2 is in P. Given a graph G on n vertices, create an algorithm that will return TRUE if  χ(G) = 2 and FALSE if  χ(G) ≠ 2. Clearly explain how your algorithm works, why it guarantees the correct output, and determine the running time of your algorithm.

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