Contractible independence complexes of trees

My Hanh Pham; Thanh Vu

Contractible independence complexes of trees

Combinatorics 2026-04-16 v2

Authors: My Hanh Pham , Thanh Vu

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 $-1$ .

Keywords

phylogenetic trees trees

Cite

@article{arxiv.2604.10269,
  title  = {Contractible independence complexes of trees},
  author = {My Hanh Pham and Thanh Vu},
  journal= {arXiv preprint arXiv:2604.10269},
  year   = {2026}
}

Comments

We are grateful to Professor Alexander Engstr\"om and Thiago Holleben for pointing out relevant work on the homotopy of the independence complexes of graphs

Contractible independence complexes of trees

Abstract

Keywords

Cite

Comments

Related papers