A simple algorithm to generate the minimal separators and the maximal cliques of a chordal graph

We present a simple unified algorithmic process which uses either LexBFS or MCS on a chordal graph to generate the minimal separators and the maximal cliques in linear time in a single pass.

► We find all the maximal cliques and minimal separators of a chordal graph.
► We unify results on algorithms MCS and LexBFS.
► A single linear-time pass is sufficient.
► We use moplexes (a generalization simplicial vertices) to prove our results.