APPROXIMATELY COHEN–MACAULAY PROPERTY OF EDGE-WEIGHTED CYCLES
DOI:
https://doi.org/10.18173/2354-1059.2026-0017Keywords:
approximately Cohen–Macaulay, edge-weighted graph, Woodroofe graphAbstract
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.
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