A method based on t-admissible subgraphs determines the regularity of the t-th symbolic power of cover ideals of graphs, applied to bipartite unicyclic graphs.
Contractible independence complexes of trees
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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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math.AC 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Critical subgraphs and the regularity of symbolic powers of cover ideals of graphs
A method based on t-admissible subgraphs determines the regularity of the t-th symbolic power of cover ideals of graphs, applied to bipartite unicyclic graphs.