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Combinatorics of the integral closure of edge ideals of strong quasi-n-partite graphs

Monica La Barbiera, Roya Moghimipor

Abstract

Combinatorial properties of some ideals related to strong quasi-n-partites graphs are examined. We prove that the edge ideal of a strong quasi-n-partite graph is not integrally closed and we give an expression for its integral closure. Moreover, we are able to determine the structure of the ideals of vertex covers for the edge ideals associated to a strong quasi-n-partite graph.

Combinatorics of the integral closure of edge ideals of strong quasi-n-partite graphs

Abstract

Combinatorial properties of some ideals related to strong quasi-n-partites graphs are examined. We prove that the edge ideal of a strong quasi-n-partite graph is not integrally closed and we give an expression for its integral closure. Moreover, we are able to determine the structure of the ideals of vertex covers for the edge ideals associated to a strong quasi-n-partite graph.
Paper Structure (2 sections, 17 theorems, 66 equations)

This paper contains 2 sections, 17 theorems, 66 equations.

Table of Contents

  1. Integral closure of edge ideals
  2. Regularity and projective dimension

Key Result

Proposition 1.5

Let $L$ be a monomial ideal of $T=K[{\bold X}]$. Then

Theorems & Definitions (41)

  • Example 1.1
  • Definition 1.2
  • Example 1.3
  • Definition 1.4
  • Proposition 1.5
  • proof
  • Proposition 1.6
  • proof
  • Definition 1.7
  • Proposition 1.8
  • ...and 31 more