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Combinatorial properties of strong quasi-n-partite graphs

Monica La Barbiera, Roya Moghimipor

Abstract

Monomial ideals corresponding to strong quasi-n-partite graphs are considered. Some algebraic and combinatorial properties of generalized graph ideals of a strong quasi-n-partite graph are studied. Furthermore, we show that the edge ideal of a strong quasi-n-partite graph is Cohen-Macaulay.

Combinatorial properties of strong quasi-n-partite graphs

Abstract

Monomial ideals corresponding to strong quasi-n-partite graphs are considered. Some algebraic and combinatorial properties of generalized graph ideals of a strong quasi-n-partite graph are studied. Furthermore, we show that the edge ideal of a strong quasi-n-partite graph is Cohen-Macaulay.
Paper Structure (3 sections, 9 theorems, 63 equations)

This paper contains 3 sections, 9 theorems, 63 equations.

Table of Contents

  1. Introduction
  2. Generalized graph ideals
  3. Monomial localizations of generalized graph ideals

Key Result

Theorem 2.7

A quasi-n-partite graph with a loop in each vertex is Cohen-Macaulay.

Theorems & Definitions (29)

  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Example 2.4
  • Remark 2.5
  • Example 2.6
  • Theorem 2.7
  • proof
  • Definition 2.8
  • Theorem 2.9
  • ...and 19 more