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arXiv · 2604.23428

Associated primes of powers of closed neighborhood ideals and diameters of graphs

Ha Thi Thu Hien·Thanh Vu
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Abstract

Let $G$ be a simple connected graph and $t \ge 2$ an integer. We prove that if the maximal homogeneous ideal is an associated prime of the $t$th power of the closed neighborhood ideal of $G$, then the diameter of $G$ is at most $7t - 8$. We further show that this bound is sharp for all $t \ge 2$.

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Ha Thi Thu Hien, Thanh Vu. 2026-04-25. Associated primes of powers of closed neighborhood ideals and diameters of graphs. https://arxiv.org/abs/2604.23428

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