Contractible independence complexes of trees
Abstract
We show that the independence complex of a tree is contractible if and only if it can be reduced to a path \( Pn \) with \( n 1 3 \) by a sequence of truncation moves at branching points. As a consequence of our method, we also characterize the trees for which the independence polynomial evaluated at \( -1 \) is equal to \( 1 \) or \( -1 \).
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