Sentence:  We show that the independence complex of a chordal graph is contractible if and only if this complex is <WSD>dismantlable</WSD> (strong collapsible) and it is homotopy equivalent to a sphere if and only if its core is a cross-polytopal sphere. 
Meaning of the word marked with <WSD> tags:  The property of a graph such that its vertices can be listed in an order such that, for every vertex, the vertex is a subdominant vertex (has an adjacent vertex that is adjacent to every other vertex that it is adjacent to) in the induced subgraph generated by that vertex and all subsequent vertices.