Very well-covered graphs via the Rees algebra (Q6566713)
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scientific article; zbMATH DE number 7875699
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Very well-covered graphs via the Rees algebra |
scientific article; zbMATH DE number 7875699 |
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Very well-covered graphs via the Rees algebra (English)
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3 July 2024
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A very well-covered graph is a well-covered (i.e. unmixed) graph without isolated vertices such that the cardinality of its minimal vertex covers is half the number of its vertices. The main result of the paper is that if \(G\) is a Cohen-Macaulay very well-covered graph, then the Rees algebra of its cover ideal is a normal Cohen-Macaulay domain. In the last section some algebraic properties of the cover ideals of whisker graphs are studied.
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Rees algebras
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normal rings
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monomial ideals
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edge ideals
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cover ideals
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very well-covered graphs
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