AbstractThe universal Gröbner basis of an ideal is a Gröbner basis with respect to all term orders simultaneously. We characterize in graph theoretical terms the elements of the universal Gröbner basis of the toric ideal of a graph. We also provide a new degree bound. Finally, we give examples of graphs for which the true degrees of their circuits are less than the degrees of some elements of the Graver basis
We consider a well-known family of polynomial ideals encoding the problem of graph k-colorability. O...
We consider a well-known family of polynomial ideals encoding the problem of graph k-colorability. O...
For all integers 4 ≤ r ≤ d, we show that there exists a finite simple graph G = Gr,d with toric idea...
AbstractThe universal Gröbner basis of an ideal is a Gröbner basis with respect to all term orders s...
Let G be a simple, undirected finite graph and I G be its corresponding toric ideal. The universal G...
Abstract. Let G be a simple graph on the vertex set {1,..., n}. An algebraic object attached to G is...
Let $G$ be a simple graph on the vertex set ${1,\ldots,n}$. An algebraic object attached to $G$ is t...
In this thesis, we study the basis sets of pure difference ideals, that is, ideals that are generate...
In this paper we prove that every toric ideal associated with a gap-free graph G has a squarefree le...
We present an algorithm which converts a given Gröbner basis of a polynomial ideal I to a Gröbner ba...
In the ring of polynomials k[x1,... ,xn] every ideal has a\ud special basis known as a Gröbner basis...
AbstractWe study the family of graphs whose number of primitive cycles equals its cycle rank. It is ...
In this paper we prove that every toric ideal associated with a gap-free graph G has a squarefree le...
We consider a well-known family of polynomial ideals encoding the problem of graph k-colorability. O...
AbstractGröbner bases are distinguished sets of generators of ideals in polynomial rings. They can b...
We consider a well-known family of polynomial ideals encoding the problem of graph k-colorability. O...
We consider a well-known family of polynomial ideals encoding the problem of graph k-colorability. O...
For all integers 4 ≤ r ≤ d, we show that there exists a finite simple graph G = Gr,d with toric idea...
AbstractThe universal Gröbner basis of an ideal is a Gröbner basis with respect to all term orders s...
Let G be a simple, undirected finite graph and I G be its corresponding toric ideal. The universal G...
Abstract. Let G be a simple graph on the vertex set {1,..., n}. An algebraic object attached to G is...
Let $G$ be a simple graph on the vertex set ${1,\ldots,n}$. An algebraic object attached to $G$ is t...
In this thesis, we study the basis sets of pure difference ideals, that is, ideals that are generate...
In this paper we prove that every toric ideal associated with a gap-free graph G has a squarefree le...
We present an algorithm which converts a given Gröbner basis of a polynomial ideal I to a Gröbner ba...
In the ring of polynomials k[x1,... ,xn] every ideal has a\ud special basis known as a Gröbner basis...
AbstractWe study the family of graphs whose number of primitive cycles equals its cycle rank. It is ...
In this paper we prove that every toric ideal associated with a gap-free graph G has a squarefree le...
We consider a well-known family of polynomial ideals encoding the problem of graph k-colorability. O...
AbstractGröbner bases are distinguished sets of generators of ideals in polynomial rings. They can b...
We consider a well-known family of polynomial ideals encoding the problem of graph k-colorability. O...
We consider a well-known family of polynomial ideals encoding the problem of graph k-colorability. O...
For all integers 4 ≤ r ≤ d, we show that there exists a finite simple graph G = Gr,d with toric idea...
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