Jahangir, RizwanRizwanJahangirVeer, DharmDharmVeer2025-08-312025-08-312025-07-0110.1007/s40840-025-01906-52-s2.0-105009547930https://d8.irins.org/handle/IITG2025/28086We characterize Cohen-Macaulay posets of dimension two; they are precisely the shellable and strongly connected posets of dimension two. We also give a combinatorial description of these posets. Using the fact that co-comparability graph of a 2-dimensional poset is a permutation graph, we characterize Cohen-Macaulay permutation graphs.falseCohen-Macaulay posets | Dimension of a poset | Permutation graph | Shellable posetsArticle21804206July 20250133arJournal0