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arXiv · 2604.10269

Contractible independence complexes of trees

My Hanh Pham·Thanh Vu
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Abstract

We show that the independence complex of a tree is contractible if and only if it can be reduced to a path \( P_n \) with \( n \equiv 1 \pmod{3} \) 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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My Hanh Pham, Thanh Vu. 2026-04-14. Contractible independence complexes of trees. https://arxiv.org/abs/2604.10269

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