Abstract
Let G be a perfect graph and let J be its ideal of vertex covers. We show that the Rees algebra of J is normal and that this algebra is Gorenstein if G is unmixed. Then we give a description–in terms of cliques–of the symbolic Rees algebra and the Simis cone of the edge ideal of G.
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Partially supported by CONACyT grant 49251-F and SNI, México.
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Villarreal, R.H. Rees algebras and polyhedral cones of ideals of vertex covers of perfect graphs. J Algebr Comb 27, 293–305 (2008). https://doi.org/10.1007/s10801-007-0088-x
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DOI: https://doi.org/10.1007/s10801-007-0088-x
Keywords
- Perfect graphs
- Normality
- Edge ideals
- Symbolic Rees algebras
- Standard Gorenstein algebras
- Max-flow min-cut
- Clutters
- Simis cone
- Hilbert basis
- Totally dual integral