A recursive construction of acyclic matchings on independence complexes for graphs with simplicial vertices yields homotopy types for chordal graphs and generalized comparability graphs via discrete Morse theory.
Independence complexes of claw-free graphs.European Journal of Combinatorics, 29(1):234–241
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A recursive construction of an acyclic matching on the independence complex of a graph with a simplicial vertex
A recursive construction of acyclic matchings on independence complexes for graphs with simplicial vertices yields homotopy types for chordal graphs and generalized comparability graphs via discrete Morse theory.