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arXiv · 2304.11630

Powers of vertex cover ideals of Simplicial Trees

Bijender·Ajay Kumar·Rajiv Kumar
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Abstract

In $2011$, Herzog, Hibi, and Ohsugi conjectured that if $J$ is the cover ideal of a chordal graph, then $J^s$ is componentwise linear for all $s \ge 1.$ In 2022, H\`a and Tuyl considered objects more general than chordal graphs and posed the following problem: Let $J(\Delta)$ be the cover ideal of a simplicial tree $\Delta.$ Is it true that $J(\Delta)^s$ is componentwise linear for all $s \geq 1$? In this article, we give an affirmative answer to this problem.

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Bijender, Ajay Kumar, Rajiv Kumar. 2023-04-23. Powers of vertex cover ideals of Simplicial Trees. https://arxiv.org/abs/2304.11630

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