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Licci Property of Complementary Edge Ideals

Vivek Bhabani Lama

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.

Licci Property of Complementary Edge Ideals

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.
Paper Structure (6 sections, 12 theorems, 11 equations)

This paper contains 6 sections, 12 theorems, 11 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Complementary Edge Ideals
  4. Erdős-Rényi Random Graphs
  5. Licci Ideals
  6. Complementary Edge Ideals and the Licci Property

Key Result

Theorem 2.1.2

ficarra2025complementary, hibi2025complementary Let $G$ be a simple graph then the following are equivalent:

Theorems & Definitions (23)

  • Definition 2.1.1
  • Theorem 2.1.2
  • Theorem 2.1.3
  • Theorem 2.1.4
  • Theorem 2.1.5
  • Theorem 2.2.1
  • Definition 2.3.1
  • Remark 2.3.2
  • Definition 2.3.3
  • Remark 2.3.4
  • ...and 13 more