scholarly journals Computing Toric Ideals

1999 ◽  
Vol 27 (4) ◽  
pp. 351-365 ◽  
Author(s):  
A.M. Bigatti ◽  
R. La Scala ◽  
L. Robbiano
Keyword(s):  
Toric Ideals

scholarly journals Toric ideals and graph theory to analyze Hopf bifurcations in mass action systems

2005 ◽  
Vol 40 (6) ◽  
pp. 1361-1382 ◽  
Author(s):  
Karin Gatermann ◽  
Markus Eiswirth ◽  
Anke Sensse
Keyword(s):  
Graph Theory ◽  
Mass Action ◽  
Hopf Bifurcations ◽  
Toric Ideals ◽  
Action Systems

scholarly journals Minimal generators of toric ideals of graphs

2012 ◽  
Vol 48 (1) ◽  
pp. 64-78 ◽  
Author(s):  
Enrique Reyes ◽  
Christos Tatakis ◽  
Apostolos Thoma
Keyword(s):  
Toric Ideals ◽  
Minimal Generators

scholarly journals Toric ideals and diagonal 2-minors

2016 ◽  
Vol 150 (1) ◽  
pp. 83-98
Author(s):  
A. Katsabekis
Keyword(s):  
Toric Ideals

Ring graphs and toric ideals

2007 ◽  
Vol 28 ◽  
pp. 393-400 ◽  
Author(s):  
Isidoro Gitler ◽  
Enrique Reyes ◽  
Rafael H. Villarreal
Keyword(s):  
Toric Ideals

scholarly journals Normal toric ideals of low codimension

2009 ◽  
Vol 213 (8) ◽  
pp. 1636-1641 ◽  
Author(s):  
Pierre Dueck ◽  
Serkan Hoşten ◽  
Bernd Sturmfels
Keyword(s):  
Toric Ideals

scholarly journals Graphs and complete intersection toric ideals

2015 ◽  
Vol 14 (09) ◽  
pp. 1540011 ◽  
Author(s):  
I. Bermejo ◽  
I. García-Marco ◽  
E. Reyes
Keyword(s):  
Complete Intersection ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Point Of View ◽  
Toric Ideals ◽  
Induced Subgraphs ◽  
Toric Ideal ◽  
Vertex Set ◽  
Combinatorial Point ◽  
Ring Graph

Our purpose is to study the family of simple undirected graphs whose toric ideal is a complete intersection from both an algorithmic and a combinatorial point of view. We obtain a polynomial time algorithm that, given a graph G, checks whether its toric ideal PG is a complete intersection or not. Whenever PG is a complete intersection, the algorithm also returns a minimal set of generators of PG. Moreover, we prove that if G is a connected graph and PG is a complete intersection, then there exist two induced subgraphs R and C of G such that the vertex set V(G) of G is the disjoint union of V(R) and V(C), where R is a bipartite ring graph and C is either the empty graph, an odd primitive cycle, or consists of two odd primitive cycles properly connected. Finally, if R is 2-connected and C is connected, we list the families of graphs whose toric ideals are complete intersection.

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