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Provide an example of a class of Markov networks Hn over n nodes for arbitrarily large n (not necessarily for every n), where the size of the largest clique is a constant independent of n, yet the size of the largest clique in any chordal graph HCn that contains Hn is exponential in n. Explain why the size of the largest clique is necessarily exponential in n for all HCn.

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