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Projective dimension and regularity of 3-path ideals of unicyclic graphs

Nguyen Thu Hang, Thanh Vu

Abstract

We compute the projective dimension and regularity of $3$-path ideals of arbitrary graphs with at most one cycle.

Projective dimension and regularity of 3-path ideals of unicyclic graphs

Abstract

We compute the projective dimension and regularity of -path ideals of arbitrary graphs with at most one cycle.
Paper Structure (9 sections, 25 theorems, 54 equations)

This paper contains 9 sections, 25 theorems, 54 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Projective dimension and regularity
  4. Betti splittings
  5. Graphs and their path ideals
  6. 3-path induced matching numbers
  7. Proximal graphs
  8. Betti splittings for 3-path ideals of graphs with at most one cycle
  9. Projective dimension and regularity of 3-path ideals of graphs with at most one cycle

Key Result

Theorem 1.1

Assume that $G$ is a connected simple graph with at most one cycle $C$ of length $m$. Then

Theorems & Definitions (55)

  • Theorem 1.1
  • Lemma 2.1
  • Definition 2.2
  • Lemma 2.3
  • proof
  • Definition 2.4
  • Lemma 2.5
  • proof
  • Lemma 2.6
  • proof
  • ...and 45 more