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Simis and packing properties of Alexander dual of connected ideals

Om Prakash Bhardwaj, Kanoy Kumar Das, Rutuja Sawant

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--Cornuèjols conjecture for this class of ideals.

Simis and packing properties of Alexander dual of connected 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--Cornuèjols conjecture for this class of ideals.
Paper Structure (3 sections, 12 theorems, 25 equations)

This paper contains 3 sections, 12 theorems, 25 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Main Results

Key Result

Theorem 1.2

Let $G$ be a connected graph on $n$ vertices and let $t\geq 3$ be an integer. Let $J_t(G)$ denote the Alexander dual of the $t$-connected ideal of $G$. Then the following statements are equivalent:

Theorems & Definitions (20)

  • Conjecture 1.1
  • Theorem 1.2: Theorem \ref{['thm: main']}
  • Theorem 2.1: 2009Gitler-et.al
  • Lemma 2.2
  • Lemma 3.1
  • proof
  • Proposition 3.2
  • proof
  • Proposition 3.3
  • proof
  • ...and 10 more