TY - JOUR

T1 - Vertex decomposability and regularity of very well-covered graphs

AU - Mahmoudi, Mohammad

AU - Mousivand, Amir

AU - Crupi, Marilena

AU - Rinaldo, Giancarlo

AU - Terai, Naoki

AU - Yassemi, Siamak

N1 - Funding Information:
Corresponding author. E-mail addresses: mahmoudi54@gmail.com (M. Mahmoudi), amirmousivand@gmail.com (A. Mousivand), mcrupi@unime.it (M. Crupi), rinaldo@dipmat.unime.it (G. Rinaldo), terai@cc.saga-u.ac.jp (N. Terai), yassemi@ipm.ir (S. Yassemi). 1 Fax: +39 090 393502. 2 Fax: +39 090 393502. 3 Siamak Yassemi was in part supported by a grant from University of Tehran.

PY - 2011/10

Y1 - 2011/10

N2 - 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.

AB - 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.

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U2 - 10.1016/j.jpaa.2011.02.005

DO - 10.1016/j.jpaa.2011.02.005

M3 - Article

AN - SCOPUS:79954632426

SN - 0022-4049

VL - 215

SP - 2473

EP - 2480

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 10

ER -