On the Topology of Independence Complexes of Triangle-Free Graphs
Jakob Jönsson · 2011
The independence complex of a (finite) simple graph is the abstract simplicial complex consisting of all independent vertex sets in the graph. We show that the possible homotopy types of independence complexes of bipartite graphs are exactly those of suspensions of simplicial complexes. As a consequence, there exist bipartite graphs such that the integral homology of the associated independence complexes is not free. This answers ˜