Vertex decomposability and regularity of very well-covered graphs

被引：47

作者：

Mahmoudi, Mohammad ^{[1
]}

Mousivand, Amir ^{[1
]}

Crupi, Marilena ^{[2
]}

Rinaldo, Giancarlo ^{[2
]}

Terai, Naoki ^{[3
]}

Yassemi, Siamak ^{[4
]}

机构：

[1] Islamic Azad Univ IAU, Dept Math, Sci & Res Branch, Tehran, Iran

[2] Univ Messina, Dipartimento Matemat, I-98166 Messina, Italy

[3] Saga Univ, Dept Math, Fac Culture & Educ, Saga 8408502, Japan

[4] Univ Tehran, Coll Sci, Sch Math Stat & Comp Sci, Tehran, Iran

来源：

JOURNAL OF PURE AND APPLIED ALGEBRA | 2011年 / 215卷 / 10期

关键词：

D O I：

10.1016/j.jpaa.2011.02.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. (C) 2011 Elsevier B.V. All rights reserved.

引用

页码：2473 / 2480

页数：8

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