On licci squarefree monomial ideals

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.