A remark on sequentially Cohen-Macaulay monomial ideals

Document Type : Research Paper

Authors

Department of Mathematics, University of Kurdistan, P.O. Box: 416, Sanandaj, Iran

10.22108/toc.2024.139193.2107

Abstract

Let $R=K[x_1,\ldots,x_n]$ be the polynomial ring in $n$ variables over a field $K$. We show that if $G$ is a connected graph with a basic $5$-cycle $C$, then $G$ is a sequentially Cohen-Macaulay graph if and only if there exists a shedding vertex $x$ of $C$ such that $G\setminus x$ and $G\setminus N[x]$ are sequentially Cohen-Macaulay graphs. Furthermore, we study the sequentially Cohen-Macaulay and Castelnuovo-Mumford regularity of square-free monomial ideals in some special cases.

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Main Subjects


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Articles in Press, Corrected Proof
Available Online from 13 May 2024
  • Receive Date: 20 September 2023
  • Revise Date: 08 May 2024
  • Accept Date: 13 May 2024
  • Published Online: 13 May 2024