In combinatorial commutative algebra, to characterize the Cohen-Macaulayness of some classes of graphs is an important topic. In this paper, we give complete characterizations for the Cohen-Macaulayness of two classes of clutters. One is interval clutters, a subclass of 𝛽-acyclic clutters; the other is 𝛽-cycles.
Li et al. (Fri,) studied this question.