Ring graphs and complete intersection toric ideals
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TLDR
The complete intersection property of toric ideals of bipartite graphs and oriented graphs was studied in this paper, where it was shown that these ideals are minimally generated by Grobner bases.About:
This article is published in Discrete Mathematics.The article was published on 2010-02-01 and is currently open access. It has received 54 citations till now. The article focuses on the topics: Chordal graph & Indifference graph.read more
Citations
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Journal ArticleDOI
Minimal generators of toric ideals of graphs
TL;DR: This work characterize in graph theoretical terms the primitive, the minimal, the indispensable and the fundamental binomials of the toric ideal I"G.
Reference BookDOI
Monomial Algebras, Second Edition
TL;DR: In this paper, the authors show how monomial algebras are related to polyhedral geometry, combinatorial optimization, and combinatorics of hypergraphs, and directly link the algebraic properties of monomial algebraic structures to combinatorical structures (such as simplicial complexes, posets, digraphs, graphs, and clutters).
Journal ArticleDOI
Properties of sut ideals associated to ring graphs
Uwe Nagel,Sonja Petrović +1 more
TL;DR: In this article, the authors studied the cut ideals of the family of ring graphs, which includes trees and cycles, and showed that they have quadratic Gr\\\"obner bases and that their coordinate rings are Koszul, Hilbertian, and Cohen-Macaulay.
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Properties of cut ideals associated to ring graphs
Uwe Nagel,Sonja Petrović +1 more
TL;DR: In this article, the authors studied the cut ideals of the family of ring graphs, which includes trees and cycles, and showed that they have quadratic Gr\"obner bases and that their coordinate rings are Koszul, Hilbertian, and Cohen-Macaulay.
Journal ArticleDOI
On complete intersection toric ideals of graphs
Christos Tatakis,Apostolos Thoma +1 more
TL;DR: In this article, it was shown that for a connected graph G such that IG is a complete intersection all of its blocks are bipartite except for at most two generators, which corresponds to two disjoint odd cycles joint at a vertex or with a path.
References
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Book
Algebraic Graph Theory
Chris Godsil,Gordon F. Royle +1 more
TL;DR: The Laplacian of a Graph and Cuts and Flows are compared to the Rank Polynomial.
Book
Graduate Texts in Mathematics
Rajendra Bhatia,Glen Bredon,Wolfgang Walter,Joseph J. Rotman,M. Ram Murty,Jane Gilman,Peter Walters,Martin Golubitsky,Ioannis Karatzas,Henri Cohen,Raoul Bott,Gaisi Takeuti,Béla Bollobás,John M. Lee,Jiří Matoušek,Saunders Mac Lane,John L. Kelley,B. A. Dubrovin,Tom M. Apostol,John Stillwell,William Arveson +20 more
Book
Graph Theory
TL;DR: Gaph Teory Fourth Edition is standard textbook of modern graph theory which covers the core material of the subject with concise yet reliably complete proofs, while offering glimpses of more advanced methods in each chapter by one or two deeper results.