On licci squarefree monomial ideals

TL;DR

This paper investigates the licci property in squarefree monomial ideals derived from graphs, providing classifications for various classes including path ideals of trees and extending known results.

Contribution

It characterizes licci properties for several classes of squarefree monomial ideals, broadening the understanding beyond edge ideals to path ideals and related structures.

Findings

Characterization of licci bi-Cohen-Macaulay squarefree monomial ideals

Full classification of licci path ideals of trees

Extension of licci classification to broader monomial ideal families

Abstract

We study the licci property for several classes of squarefree monomial ideals arising from graphs and related combinatorial structures. We characterize licci bi-Cohen-Macaulay squarefree monomial ideals, complementary edge ideals, $t$-path ideals of cycles, and $(t-1)$-suspensions of graphs. Consequently, the full list of licci path ideals of trees is obtained. This work extends the known classification of licci edge ideals to a broader family of path ideals.