Shellable graphs and sequentially Cohen–Macaulay bipartite graphs

Associated to a simple undirected graph G is a simplicial complex ΔG whose faces correspond to the independent sets of G. We call a graph G shellable if ΔG is a shellable simplicial complex in the non-pure sense of Björner–Wachs. We are then interested in determining what families of graphs have the property that G is shellable. We show that all chordal graphs are shellable. Furthermore, we classify all the shellable bipartite graphs; they are …