50 research outputs found

    Cohen-Macaulay Weighted Oriented Chordal and Simplicial Graphs

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    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.Comment: 7 pages, 1 figur

    Second powers of cover ideals of paths

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    We show that the second power of the cover ideal of a path graph has linear quotients. To prove our result we construct a recursively defined order on the generators of the ideal which yields linear quotients. Our construction has a natural generalization to the larger class of chordal graphs. This generalization allows us to raise some questions that are related to some open problems about powers of cover ideals of chordal graphs.Comment: revised, 19 pages, 3 figure

    Cohen-Macaulay weighted chordal graphs

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    In this paper I give a combinatorial characterization of all the Cohen-Macaulay weighted chordal graphs. In particular, it is shown that a weighted chordal graph is Cohen- Macaulay if and only if it is unmixed

    Powers of componentwise linear ideals

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    We give criteria for graded ideals to have the property that all their powers are componentwise linear. Typical examples to which our criteria can be applied include the vertex cover ideals of certain finite graphs
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