Question: Suppose we are given a graph G as well as a color cv for each vertex v . The task is to find the longest

Suppose we are given a graph G as well as a color cv for each vertex v. The task is to find the longest path in the graph which consists of all different colours (i.e. no two vertices along the path share a colour).
1. State a decision version of the problem.
2. Show it is in NP.
3. Show it is NP-hard. Conclude it is NP-complete.

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