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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| Дата: | 2010 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2010
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/154873 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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dspace |
| spelling |
irk-123456789-1548732019-06-17T01:31:23Z Symbolic Rees algebras, vertex covers and irreducible representations of Rees cones Dupont, L.D. Villarreal, R.H. 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. 2010 Article 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 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Dupont, L.D. Villarreal, R.H. |
| spellingShingle |
Dupont, L.D. Villarreal, R.H. Symbolic Rees algebras, vertex covers and irreducible representations of Rees cones Algebra and Discrete Mathematics |
| author_facet |
Dupont, L.D. Villarreal, R.H. |
| author_sort |
Dupont, L.D. |
| title |
Symbolic Rees algebras, vertex covers and irreducible representations of Rees cones |
| 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 |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2010 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Algebra and Discrete Mathematics |
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2023-05-20T17:45:27Z |
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2023-05-20T17:45:27Z |
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