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.
Combinatorial realization of the thom-smale complex via discrete Morse theory.Annali della Scuola Normale Superiore di Pisa-Classe di Scienze, 9(2):229–252,
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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.