  We introduce a method to reduce the study of the topology of a simplicial
complex to that of a simpler one. We give some applications of this method to
complexes arising from graphs. As a consequence, we answer some questions
raised in [R.Ehrenborg, G.Hetyei, European J.Combin.27 (2006), no.6, 906-923]
on the independence complex and the dominance complex. The techniques used come
mainly from monomial ideal theory.
