Vertex decomposability and regularity of very well-covered graphs
Journal of Pure and Applied Algebra, 2011•Elsevier
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.
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.
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.
Elsevier