INDEPENDENCE COMPLEXES OF STRONGLY ORDERABLE GRAPHS

We prove that for any finite strongly orderable (generalized strongly chordal) graph G, the independence complex Ind(G) is either contractible or homotopy equivalent to a wedge of spheres of dimension at least bp(G) - 1, where bp(G) is the biclique vertex partition number of G. In particular, we show that if G is a chordal bipartite graph, then Ind(G) is either contractible or homotopy equivalent to a sphere of dimension at least bp(G) - 1.