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Powers of vertex cover ideals of simplicial trees

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  • Bijender
  • Ajay Kumar
  • Rajiv Kumar

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.

Suggested Citation

  • Bijender & Ajay Kumar & Rajiv Kumar, 2024. "Powers of vertex cover ideals of simplicial trees," Mathematische Nachrichten, Wiley Blackwell, vol. 297(3), pages 1116-1135, March.
    • Handle: RePEc:bla:mathna:v:297:y:2024:i:3:p:1116-1135
    DOI: 10.1002/mana.202200510
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