Cohen-Macaulay edge ideal whose height is half of the number of vertices

TL;DR

This paper characterizes Cohen-Macaulay graphs where the edge ideal's height is exactly half the number of vertices, providing specific criteria for such graphs.

Contribution

It introduces Cohen-Macaulay criteria for graphs with edge ideals of height half the number of vertices, a novel class in algebraic graph theory.

Findings

Provides necessary and sufficient conditions for Cohen-Macaulayness in this class

Identifies structural properties of graphs with this edge ideal height

Advances understanding of algebraic properties linked to graph structure

Abstract

We consider a class of graphs $G$ such that the height of the edge ideal $I(G)$ is half of the number $\sharp V(G)$ of the vertices. We give Cohen-Macaulay criteria for such graphs.