5. The non-dominating independence complex of G, denoted I'(G), is the abstract simplicial complex of the independent sets that are not dominating sets of G. Obviously I'(G) is contained in I(G); denote the inclusion map by i: I'(G)\to I(G). If G is a chordal graph then the induced map i_*: \tilde{H}_k(I'(G))\to \tilde{H}_k(I(G)) is zero for all k\geq -1. This is a generalization of property 3 above.
