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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| Опубліковано в: : | Algebra and Discrete Mathematics |
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| Дата: | 2010 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2010
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| Онлайн доступ: | https://nasplib.isofts.kiev.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| _version_ | 1862623479647436800 |
|---|---|
| author | Dupont, L.D. Villarreal, R.H. |
| author_facet | Dupont, L.D. Villarreal, R.H. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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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| first_indexed | 2025-12-07T13:29:19Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-154873 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| language | English |
| last_indexed | 2025-12-07T13:29:19Z |
| publishDate | 2010 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | Symbolic Rees algebras, vertex covers and irreducible representations of Rees cones Dupont, L.D. Villarreal, R.H. |
| title | 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_short | Symbolic Rees algebras, vertex covers and irreducible representations of Rees cones |
| title_sort | symbolic rees algebras, vertex covers and irreducible representations of rees cones |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/154873 |
| work_keys_str_mv | AT dupontld symbolicreesalgebrasvertexcoversandirreduciblerepresentationsofreescones AT villarrealrh symbolicreesalgebrasvertexcoversandirreduciblerepresentationsofreescones |