Запис Детальніше

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
 
Creator Dupont, L.D.
Villarreal, R.H.
 
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.
 
Date 2019-06-16T05:57:26Z
2019-06-16T05:57:26Z
2010
 
Type Article
 
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
 
Language en
 
Relation Algebra and Discrete Mathematics
 
Publisher Інститут прикладної математики і механіки НАН України