# Cohen-Macaulay binomial edge ideals of cactus graphs

## TL;DR

This paper classifies when binomial edge ideals of cactus and bicyclic graphs are Cohen-Macaulay, providing a clear characterization for these classes of graphs.

## Contribution

It offers a complete classification of Cohen-Macaulay binomial edge ideals specifically for cactus and bicyclic graphs, advancing understanding in algebraic graph theory.

## Key findings

- Cohen-Macaulay binomial edge ideals are characterized for cactus graphs.
- Cohen-Macaulay binomial edge ideals are characterized for bicyclic graphs.
- Provides a classification framework for these graph classes.

## Abstract

We classify the Cohen-Macaulay binomial edge ideals of cactus and bicyclic graphs.