Contractible independence complexes of trees
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908964723097600 |
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| author | Pham, My Hanh Vu, Thanh |
| author_facet | Pham, My Hanh Vu, Thanh |
| contents | 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 \( -1 \). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_10269 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Contractible independence complexes of trees Pham, My Hanh Vu, Thanh Combinatorics 05C31, 05C69 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 \( -1 \). |
| title | Contractible independence complexes of trees |
| topic | Combinatorics 05C31, 05C69 |
| url | https://arxiv.org/abs/2604.10269 |