A Note on Independence Complexes of Chordal Graphs and Dismantling
Michał Adamaszek · The Electronic Journal of Combinatorics · 2017
We show that the independence complex of a chordal graph is contractible if and only if this complex is dismantlable (strong collapsible) and it is homotopy equivalent to a sphere if and only if its core is a cross-polytopal sphere. The proof uses the properties of tree models of chordal graphs.