Algebraic implications of neighborhood hypergraphs and their transversal hypergraphs

Abstract

In this paper, we unfold balanced and totally balanced neighborhood hypergraphs to discover new classes of normally torsion-free monomial ideals. As a consequence, we establish that the closed neighborhood ideals and the dominating ideals of strongly chordal graphs are normally torsion-free. We discuss the stable sets of associated primes of the dominating ideals of cycles and characterize all the cycles with normally torsion-free dominating ideals.

KEYWORDS:

• Closed neighborhood ideals
• cycles
• dominating ideals
• normally torsion-freeness
• strongly chordal graphs

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 13B25
• 13F20
• 05C25
• 05E40

Acknowledgments

The authors are deeply grateful to the anonymous referee for her/his careful reading of the manuscript and for her/his valuable, detailed and informative suggestions and comments on this manuscript.

Data availability statement

My manuscript has no associate data.

Disclosure statement

There are no financial or non-financial competing interests.

Additional information

Funding

Ayesha Asloob Qureshi is supported by The Scientific and Technological Research Council of Turkey - TÜBITAK (Grant No: 122F128), and acknowledge support from the ICTP through the Associates Programme (2019-2023).