Licci Property of Complementary Edge Ideals

TL;DR

This paper characterizes when complementary edge ideals of graphs have the licci property, linking algebraic and graph-theoretic features, and explores probabilistic regimes for random graphs.

Contribution

It provides a graph-based characterization of the licci property for complementary edge ideals and analyzes probabilistic conditions for random graphs.

Findings

Complementary edge ideals are licci under specific graph conditions.

High probability regimes for licci property in random graphs identified.

Non-licci regimes also characterized probabilistically.

Abstract

In this article, we characterize the class of complementary edge ideals which satisfy the licci property in terms of the underlying graph. Using this characterization, we associate the licci property of a complementary edge ideal to its other algebraic properties. Finally, we provide two different probability regimes for which the complementary edge ideals of random graphs are licci with high probability and not licci with high probability respectively.