Symbolic Rees algebras, vertex covers and irreducible representations of Rees cones
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...
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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2010 |
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| Sprache: | English |
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Інститут прикладної математики і механіки НАН України
2010
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| Zitieren: | 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. |
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Dupont, L.D. Villarreal, R.H. 2019-06-16T05:57:26Z 2019-06-16T05:57:26Z 2010 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. https://nasplib.isofts.kiev.ua/handle/123456789/154873 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. Partially supported by CONACyT grant 49251-F and SNI, M ́exico en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Symbolic Rees algebras, vertex covers and irreducible representations of Rees cones Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Symbolic Rees algebras, vertex covers and irreducible representations of Rees cones |
| spellingShingle |
Symbolic Rees algebras, vertex covers and irreducible representations of Rees cones Dupont, L.D. Villarreal, R.H. |
| title_short |
Symbolic Rees algebras, vertex covers and irreducible representations of Rees cones |
| title_full |
Symbolic Rees algebras, vertex covers and irreducible representations of Rees cones |
| title_fullStr |
Symbolic Rees algebras, vertex covers and irreducible representations of Rees cones |
| title_full_unstemmed |
Symbolic Rees algebras, vertex covers and irreducible representations of Rees cones |
| title_sort |
symbolic rees algebras, vertex covers and irreducible representations of rees cones |
| author |
Dupont, L.D. Villarreal, R.H. |
| author_facet |
Dupont, L.D. Villarreal, R.H. |
| publishDate |
2010 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| 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.
|
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/154873 |
| citation_txt |
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. |
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2025-12-07T13:29:19Z |
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2025-12-07T13:29:19Z |
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1850856344532287488 |