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A Characterization of Edge Ideals with $reg(R/I(G)) = 3$

Akane Kanno

Abstract

Let $G$ be a graph and $I(G)$ its edge ideal. In this paper, we give a complete characterization of the graphs $G$ for which $\reg(R/I(G)) = 3$.

A Characterization of Edge Ideals with $reg(R/I(G)) = 3$

Abstract

Let be a graph and its edge ideal. In this paper, we give a complete characterization of the graphs for which .
Paper Structure (2 sections, 14 theorems, 29 equations)

This paper contains 2 sections, 14 theorems, 29 equations.

Table of Contents

  1. Preliminaries
  2. Main Result

Key Result

Theorem 1

Let $\operatorname{m}(G)$ denote the matching number of $G$, and $\operatorname{im}(G)$ the induced matching number of $G$. Then the following inequalities hold:

Theorems & Definitions (18)

  • Theorem 1: W Lemma 7, HVT, Theorem 6.7, and K, Lemma 2.2
  • Theorem 2: F
  • Theorem 3: F
  • Theorem 4: FRG, Theorem 3.1
  • Theorem 1.1: HVT, Theorem 6.7, and K, Lemma 2.2
  • Lemma 1.2: Peeva, Proposition 18.6
  • Theorem 1.3
  • Theorem 1.4: DHS, Lemma 2.10
  • Lemma 1.5
  • proof
  • ...and 8 more