Cohen-Macaulay permutation graphs - Cheri, P. V.; Dey, Deblina; K, Akhil; Kotal, Nirmal; Veer, Dharm (MATHEMATICA SCANDINAVICA, 2024)
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.