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The sequentially Cohen-Macaulay property of edge ideals of edge-weighted graphs
Published 9 Aug 2023 in math.AC | (2308.05020v1)
Abstract: Let $I(G_{\mathbf{w}})$ be the edge ideal of an edge-weighted graph $(G,\mathbf{w})$. We prove that $I(G_{\mathbf{w}})$ is sequentially Cohen-Macaulay for all weight functions $w$ if and only if $G$ is a Woodroofe graph.
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