English

Cohen-Macaulay Weighted Oriented Chordal and Simplicial Graphs

Commutative Algebra 2023-08-14 v2 Combinatorics

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.

Keywords

Cite

@article{arxiv.2307.10416,
  title  = {Cohen-Macaulay Weighted Oriented Chordal and Simplicial Graphs},
  author = {Kamalesh Saha},
  journal= {arXiv preprint arXiv:2307.10416},
  year   = {2023}
}

Comments

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)

R2 v1 2026-06-28T11:35:17.408Z