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arXiv · 2307.10416

Cohen-Macaulay Weighted Oriented Chordal and Simplicial Graphs

Kamalesh Saha
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Abstract

Herzog, Hibi, and Zheng classified the Cohen-Macaulay edge ideals of chordal graphs. In this paper, we classify Cohen-Macaulay edge ideals of (vertex) weighted oriented chordal and simplicial graphs, a more general class of monomial ideals. In particular, we show that the Cohen-Macaulay property of these ideals is equivalent to the unmixed one and hence, independent of the underlying field.

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Kamalesh Saha. 2023-08-11. Cohen-Macaulay Weighted Oriented Chordal and Simplicial Graphs. https://arxiv.org/abs/2307.10416

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