Provide an example of a class of markov networks hn over n

Question

Problem

Provide an example of a class of Markov networks H_n 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 H^C_n that contains H_n is exponential in n. Explain why the size of the largest clique is necessarily exponential in n for all H^C_n.