Cohen-Macaulay oriented graphs with large girth

TL;DR

This paper classifies Cohen-Macaulay weighted oriented graphs with underlying graphs of girth at least 5, advancing understanding of their algebraic and combinatorial properties.

Contribution

It provides a complete classification of Cohen-Macaulay weighted oriented graphs with large girth, a previously unexplored class.

Findings

Classification of Cohen-Macaulay graphs with girth ≥ 5

Characterization of algebraic properties of these graphs

Extension of Cohen-Macaulay graph theory

Abstract

We classify the Cohen-Macaulay weighted oriented graphs whose underlying graphs have girth at least $5$.