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. Wefirst 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.
Vertex decomposability and regularity of very well-covered graphs
CRUPI, Marilena;RINALDO, GIANCARLO;
2011-01-01
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. Wefirst 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.File in questo prodotto:
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