# Squarefree monomial ideals with maximal depth

## TL;DR

This paper classifies squarefree monomial ideals with maximal depth, including edge ideals of cycle graphs, transversal polymatroidal ideals, and high powers of connected bipartite graph ideals, revealing their structural properties.

## Contribution

It provides a classification of squarefree monomial ideals with maximal depth, expanding understanding of their algebraic and combinatorial characteristics.

## Key findings

- Classified edge ideals of cycle graphs with maximal depth
- Identified transversal polymatroidal ideals with this property
- Analyzed high powers of connected bipartite graph ideals

## Abstract

Let $(R,\mm)$ be a Noetherian local ring and $M$ a finitely generated $R$-module. We say $M$ has maximal depth if there is an associated prime $\pp$ of $M$ such that $\depth M=\dim R/\pp$. In this paper we study squarefree monomial ideals which have maximal depth. Edge ideals of cycle graphs, transversal polymatroidal ideals and high powers of connected bipartite graph with this property are classified.