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arXiv · 2609.36674

Weak and strong Lefschetz properties for vertex cover Artinian algebras associated to graphs

Trung Chau·Tran Quang Hoa·Dang Thi Kieu Uyen
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Abstract

Let $G$ be a finite simple graph and let $A_c(G)$ be the Artinian algebra associated with its cover ideal. We prove that $A_c(G)$ has the WLP when $τ(G)>|V(G)|/2$, where $τ(G)$ denotes the size of a minimum vertex cover of $G$. As a consequence, $A_c(G)$ has the WLP with high probability when the Erdős-Rényi random graph model is considered. Moreover, we study the borderline case $τ(G)=|V(G)|/2$ and as a result, classify the WLP for paths, cycles, Ferrers graphs, and well-covered trees.

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Trung Chau, Tran Quang Hoa, Dang Thi Kieu Uyen. 2026-09-29. Weak and strong Lefschetz properties for vertex cover Artinian algebras associated to graphs. https://arxiv.org/abs/2609.36674

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