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math.AC2026
Geometrically vertex decomposable open neighborhood ideals
Jounglag Lim
In this paper, we prove that the open neighborhood ideal of a TD-unmixed tree is geometrically vertex decomposable. This result implies that the associated Stanley-Reisner complex…
math.AC2025
Open Neighborhood Ideals of Well-Totally Dominated Trees are Cohen-Macaulay
Jounglag Lim, James Gossell, Keri Ann Sather-Wagstaff
We introduce and investigate the open neighborhood ideal of a finite simple graph . We describe the minimal primary decomposition of in terms o…