Vertex decomposability and regularity of very well-covered graphs

Mohammad Mahmoudi, Amir Mousivand, Marilena Crupi, Giancarlo Rinaldo, Naoki Terai, Siamak Yassemi

Research output: Contribution to journalArticle

30 Citations (Scopus)

Abstract

A graph is called very well-covered if it is unmixed without isolated vertices such that the cardinality of each minimal vertex cover is half the number of vertices. We first prove that a very well-covered graph is Cohen-Macaulay if and only if it is vertex decomposable. Next, we show that the Castelnuovo-Mumford regularity of the quotient ring of the edge ideal of a very well-covered graph is equal to the maximum number of pairwise 3-disjoint edges.

Original languageEnglish
Pages (from-to)2473-2480
Number of pages8
JournalJournal of Pure and Applied Algebra
Volume215
Issue number10
DOIs
Publication statusPublished - Oct 2011
Externally publishedYes

ASJC Scopus subject areas

  • Algebra and Number Theory

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