Cores of simplicial complexes
We introduce a method to reduce the study of the topology of a simplicial complex to that of a simpler one. Applying this method to complexes arising from graphs, we give topological meaning to classical graph invariants. As a consequence, we answer some questions raised in (Ehrenborg and Hetyei in Eur. J. Comb. 27(6):906-923, 2006) on the independence complex and the dominance complex of a forest and obtain improved algorithms to compute their homotopy types.
simplicial complexes homotopy type monomial ideals independence and domination in forests