Simis and packing properties of Alexander dual of connected ideals

TL;DR

This paper classifies graphs whose connected ideals have coinciding ordinary and symbolic powers of their Alexander duals and proves a related conjecture for this class.

Contribution

It provides a complete classification of such graphs and confirms the Conforti--Cornu extbackslash`ejols conjecture for their associated ideals.

Findings

Identified conditions for equality of powers of Alexander duals of connected ideals.

Classified all graphs with this property.

Proved the Conforti--Cornu extbackslash`ejols conjecture for these ideals.

Abstract

In this article, we investigate when the ordinary and symbolic powers of the Alexander dual of connected ideals of graphs coincide, and provide a complete classification of all such graphs. Furthermore, we prove Conforti--Cornu\`ejols conjecture for this class of ideals.