In this paper we present a unifying approach to study the homotopy type of several complexes arising from forests. We show that this method applies uniformly to many complexes that have been extensively studied in the recent years.
We introduce and study the notions of conical and spherical graphs. We show that these mutually exclusive properties, which have a geometric interpretation , provide links between apparently unrelated classical concepts such as dominating sets, independent dominating sets, edge covers, and the homotopy type of an associated simplicial complex. In… (More)