Symbolic Rees algebras, vertex covers and irreducible representations of Rees cones
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Symbolic Rees algebras, vertex covers and irreducible representations of Rees cones
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| Creator |
Dupont, L.D.
Villarreal, R.H. |
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| Description |
Let G be a simple graph and let Ic(G) be its ideal of vertex covers. We give a graph theoretical description of the irreducible b-vertex covers of G, i.e., we describe the minimal generators of the symbolic Rees algebra of Ic(G). Then we study the irreducible b-vertex covers of the blocker of G, i.e., we study the minimal generators of the symbolic Rees algebra of the edge ideal of G. We give a graph theoretical description of the irreducible binary b-vertex covers of the blocker of G. It is shown that they correspond to irreducible induced subgraphs of G. As a byproduct we obtain a method, using Hilbert bases, to obtain all irreducible induced subgraphs of G. In particular we obtain all odd holes and antiholes. We study irreducible graphs and give a method to construct irreducible b-vertex covers of the blocker of G with high degree relative to the number of vertices of G.
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| Date |
2019-06-16T05:57:26Z
2019-06-16T05:57:26Z 2010 |
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| Type |
Article
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| Identifier |
Symbolic Rees algebras, vertex covers and irreducible representations of Rees cones / L.A. Dupont, R.H. Villarreal // Algebra and Discrete Mathematics. — 2010. — Vol. 10, № 2. — С. 64–86. — Бібліогр.: 30 назв. — англ.
2000 Mathematics Subject Classification:13F20, 05C75, 05C65, 52B20. http://dspace.nbuv.gov.ua/handle/123456789/154873 |
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| Language |
en
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| Relation |
Algebra and Discrete Mathematics
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| Publisher |
Інститут прикладної математики і механіки НАН України
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