APPROXIMATELY COHEN–MACAULAY PROPERTY OF EDGE-WEIGHTED CYCLES - Ha Son, Phan (HNUE Journal of Science: Journal of Natural Sciences, 2026)
In this paper, we investigate the approximately Cohen-Macaulay property of edge ideals associated with edge-weighted graphs. Our main result establishes that the edge ideal I(Cn,w) of an edge-weighted cycle graph of order n is approximately Cohen-Macaulay if and only if n = 3 or n = 5. The proof heavily relies on the algebraic properties of sequentially Cohen-Macaulay modules, Woodroofe graphs, and Goto’s characterization of approximately Cohen-Macaulay rings.