Cohen-Macaulay Weighted Oriented Chordal and Simplicial Graphs

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.

Lemma 3.1 of the version 1 was wrong and the proof of Theorem 3.2 (v1) has been modified and became Theorem 3.1 in (v2)