  In this article, we characterize Cohen-Macaulay permutation graphs. In
particular, we show that a permutation graph is Cohen-Macaulay if and only if
it is well-covered and there exists a unique way of partitioning its vertex set
into $r$ disjoint maximal cliques, where $r$ is the cardinality of a maximal
independent set of the graph. We also provide some sufficient conditions for a
comparability graph to be a uniquely partially orderable (UPO) graph.
