  We generalize some homotopy calculation techniques such as splittings and
matching trees that are introduced for the computations in the case of the
independence complexes of graphs to arbitrary simplicial complexes, and
exemplify their efficiency on some simplicial complexes, the devoid complexes
of graphs, which are simplicial complexes parametrized by graphs. Additionally,
we compute the homotopy type of dominance complexes of chordal graphs.
