Jahangir, RizwanRizwanJahangirVeer, DharmDharmVeer2025-08-282025-08-282023-05-01http://arxiv.org/abs/2305.04535http://repository.iitgn.ac.in/handle/IITG2025/20150We 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.en-USCohen-Macaulay posetsPermutation graphsCo-comparability graphShellableStanley-Reisner theorye-Printe-Print123456789/555