Problem
1. Provide a simple method for constructing a clique tree such that a given set of variables Y is guaranteed to be to together in some clique. Your algorithm should use a standard clique-tree construction algorithm as a black box.
2. Assume that we have a clique tree T over X such that, for every pair of nodes X, Y ∈ X , there exists a clique that contains both X and Y . Prove that T must contain a single clique that contains all of X.