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In this paper we characterize chordal graphs in which:
(i) Every perfect elimination ordering (PEO) can be generated by MCS algorithm.
(ii) Every PEO can be generated by LEX-BFS algorithm,
(iii) Every PEO can be generated by MCS algorithm as well as LEX-BFS algorithm, and
(iv) Every ordering generated by LEX-BFS algorithm can also be generated by MCS algorithm and vice versa.