Moplex elimination orderings

Classically, triangulated graphs are characterized and recognized by way of perfect elimination orderings (peo, which correspond to an elimination scheme on simplicial vertices). Algorithm LexBFS computes such a peo efficiently, but is also useful for the enumeration of the minimal separators and maximal cliques, which means that the ordering it produces is special. sent an ordering which generalizes a LexBFS-type ordering, by eliminating at each step a set of simplicial vertices (called a moplex). This type of ordering actually characterizes triangulated graphs and easily yields the minimal separators and maximal cliques. ablish a strong relationship between moplex elimination orderings and clique trees. We also extend our results to the problem of embedding an arbitrary graph into a triangulated graph by showing that this process of computing a minimal triangulation is essentially equivalent to forcing a graph into having a simplicial moplex elimination ordering