The facet ideals of matching complexes of line graphs

TL;DR

This paper investigates the algebraic properties of facet ideals derived from matching complexes of line graphs, providing explicit decompositions and formulas for key invariants like projective dimension and regularity.

Contribution

It offers the first explicit irreducible decomposition and exact formulas for projective dimension and regularity of facet ideals of matching complexes of line graphs.

Findings

Irreducible decomposition of the facet ideal $(L_n)$ is obtained.

Exact formulas for projective dimension and regularity are derived.

Results enhance understanding of algebraic invariants of matching complexes.

Abstract

Let $L_n$ be a line graph with $n$ edges and $\F(L_n)$ the facet ideal of its matching complex. In this paper, we provide the irreducible decomposition of $\F(L_n)$ and some exact formulas for the projective dimension and the regularity of $\F(L_n)$.