The paper demonstrates a method to determine contractibility or sphere equivalence in independence complexes of forests, supporting topological understanding.
Ehrenborg and Hetyei proved that the independence complex of an arbitrary forest is either contractible or homotopy equivalent to a sphere. The present paper provides an inductive method of detecting the contractibility of the complex or the dimension of the sphere to which the complex is homotopy equivalent.
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Kazuhiro Kawamura (2010) studied this question.
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