Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Forests whose matching powers are linear

Nursel Erey, Antonino Ficarra

Abstract

In this note, we classify all the weighted oriented forests whose edge ideals have the property that one of their matching powers has linear resolution.

Forests whose matching powers are linear

Abstract

In this note, we classify all the weighted oriented forests whose edge ideals have the property that one of their matching powers has linear resolution.
Paper Structure (3 sections, 5 theorems, 13 equations, 5 figures)

This paper contains 3 sections, 5 theorems, 13 equations, 5 figures.

Table of Contents

  1. The last matching power of a quadratic monomial ideal
  2. Linearly related matching powers
  3. Forests whose last matching power is polymatroidal

Key Result

Theorem 1.1

Let $G$ be a finite simple graph. Then $I(G)^{[\nu(G)]}$ is polymatroidal.

Figures (5)

  • Figure 1: A forest $G$ with distant configuration $(a_1,\dots,a_t\ |\ b,c)$.
  • Figure :
  • Figure :
  • Figure :
  • Figure :

Theorems & Definitions (9)

  • Theorem 1.1
  • proof
  • Remark 2.1
  • Lemma 2.2
  • Theorem 2.3
  • Lemma 3.1
  • proof
  • Theorem 3.2
  • proof