50 research outputs found
Cohen-Macaulay Weighted Oriented Chordal and Simplicial Graphs
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
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
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
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