# Almost normally torsionfree ideals

## TL;DR

This paper characterizes connected graphs and specific algebraic structures whose edge and facet ideals are almost normally torsionfree, expanding understanding of algebraic properties in combinatorial and algebraic graph theory.

## Contribution

It provides a complete description of connected graphs with almost normally torsionfree edge ideals and analyzes special odd cycles and t-spread principal Borel ideals.

## Key findings

- Connected graphs with almost normally torsionfree edge ideals are fully characterized.
- Facet ideals of certain odd cycles are shown to be almost normally torsionfree.
- Specific t-spread principal Borel ideals generated in degree 3 are identified as almost normally torsionfree.

## Abstract

We describe all connected graphs whose edge ideals are almost normally torsionfree. We also prove that the facet ideal of a special odd cycle is almost normally torsionfree. Finally, we determine the t-spread principal Borel ideals generated in degree 3 which are almost normally torsionfree.