Powers of vertex cover ideals of simplicial trees

Bijender, Ajay Kumar and Rajiv Kumar

Mathematische Nachrichten, 2024, vol. 297, issue 3, 1116-1135

Abstract: In 2011, Herzog et al. conjectured that if J$J$ is the cover ideal of a chordal graph, then Js$J^s$ is componentwise linear for all s≥1$s \ge 1$. In 2022, Hà and Van Tuyl considered objects more general than chordal graphs and posed the following problem: let J(Γ)$J(\Gamma )$ be the cover ideal of a simplicial tree Γ$\Gamma$. Is it true that J(Γ)s$J(\Gamma )^s$ is componentwise linear for all s≥1?$s \ge 1?$ In this paper, we give an affirmative answer to this problem.

Date: 2024
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