Papers › Collapsibility and homological properties of ℑ-contractible transformations
Collapsibility and homological properties of ℑ-contractible transformations
Jesus F. Espinoza, Martín-Eduardo Frías-Armenta, Héctor A. Hernández
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The family of ℑ-contractible graphs and contractible transformations was defined by A. Ivashchenko in the mid-90's. In this paper we study the collapsibility and homological properties of the clique complex associated to ℑ-contractible graphs. We show that for any graph in a special subfamily of the ℑ-contractible graphs (the strong ℑ-contractible ones) its clique complex is collapsible. Moreover, we present an algorithm that allows us to verify if any graph is strong ℑ-contractible, as well as an algorithm to delete those vertices whose open neighborhood is also strong ℑ-contractible. Finally, we show how to use these algorithms to compute the persistent homology of an arbitrary Vietoris-Rips complex for applications in topological data analysis.
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