8 citations · 26 across the 10 of their papers we have counts for
11 papers
Unimodular toric ideals of graphs
Christos Tatakis
We give a necessary and sufficient graph-theoretic characterization of toric ideals of graphs that are unimodular. As a direct consequence, we provide the structure of unimodular g…
Toric ideals of graphs minimally generated by a Gröbner basis
Ignacio García-Marco, Irene Márquez-Corbella, Christos Tatakis
Describing families of ideals that are minimally generated by at least one, or by all, of their reduced Gröbner bases is a central topic in commutative algebra. In this paper, we a…
Universally free numerical semigroups
Ignacio García Marco, Pedro A. García-Sánchez, Ignacio Ojeda +1
A numerical semigroup is said to be universally free if it is free for any possible arrangement of its minimal generating set. In this work, we establish that toric ideals associat…
On robustness and related properties on toric ideals
Christos Tatakis, Ignacio García-Marco
A toric ideal is called robust if its universal Gröbner basis is a minimal set of generators, and is called generalized robust if its universal Gröbner basis equals its universal M…
On the relative size of toric bases
Christos Tatakis, Apostolos Thoma
We consider the Graver basis, the universal Groebner basis, a Markov basis and the set of the circuits of a toric ideal. Let be any two of these bases such that $A\not \subs…
Generalized robust toric ideals
Christos Tatakis
An ideal I is robust if its universal Gröbner basis is a minimal generating set for this ideal. In this paper, we generalize the meaning of robust ideals. An ideal is defined as ge…
An algorithm for computing the universal Gröbner Basis of graph ideals
Yannis C. Stamatiou, Christos Tatakis
The universal Gröbner basis of an ideal is a Gröbner basis with respect to all term orders simultaneously. The aim of this paper is to present an algorithmic approach to compute th…
Graver degrees are not polynomially bounded by true circuit degrees
Christos Tatakis, Apostolos Thoma
Let be a toric ideal. We prove that the degrees of the elements of the Graver basis of are not polynomially bounded by the true degrees of the circuits of .
On Complete Intersection toric ideals of graphs
Christos Tatakis, Apostolos Thoma
We characterize the graphs for which their toric ideals are complete intersections. In particular we prove that for a connected graph such that is complete inte…
On the universal Gröbner bases of toric ideals of graphs
Christos Tatakis, Apostolos Thoma
The universal Gröbner basis of , is a Gröbner basis for with respect to all term orders simultaneously. Let be the toric ideal of a graph . We characterize in graph…
Minimal generators of toric ideals of graphs
Enrique Reyes, Christos Tatakis, Apostolos Thoma
Let be the toric ideal of a graph . We characterize in graph theoretical terms the primitive, the minimal, the indispensable and the fundamental binomials of the toric ide…