A combinatorial characterization of the 1-skeletons of the Cohen–Macaulay complexes of dimension 2 over Z will be given. We also give an example of a graph that cannot be the 1-skeleton of any shellable complex of dimension 2 and an example of a graph that can only be the 1-skeleton of a Cohen–Macaulay complex over a field of some particular characteristic.
Document Type: Research Article
Department of Computer Science, Ritsumeikan University, Nojihigashi 1-1-1, Shiga, 525-8577, Japan 2:
Graduate School of Science, Osaka University, Osaka, 560, Japan