  Algorithm MLS (Maximal Label Search) is a graph search algorithm which
generalizes algorithms MCS, LexBFS, LexDFS and MNS. On a chordal graph, MLS
computes a peo (perfect elimination ordering) of the graph. We show how
algorithm MLS can be modified to compute a pmo (perfect moplex ordering) as
well as a clique tree and the minimal separators of a chordal graph. We give a
necessary and sufficient condition on the labeling structure for the beginning
of a new clique in the clique tree to be detected by a condition on labels. MLS
is also used to compute a clique tree of the complement graph, and new cliques
in the complement graph can be detected by a condition on labels for any
labeling structure. A linear time algorithm computing a pmo and the generators
of the maximal cliques and minimal separators w.r.t. this pmo of the complement
graph is provided. On a non-chordal graph, algorithm MLSM is used to compute an
atom tree of the clique minimal separator decomposition of any graph.
