Name
Abstract | ||
|---|---|---|
We study the family of graphs whose number of primitive cycles equals its cycle rank. It is shown that this family is precisely the family of ring graphs. Then we study the complete intersection property of toric ideals of bipartite graphs and oriented graphs. An interesting application is that complete intersection toric ideals of bipartite graphs correspond to ring graphs and that these ideals are minimally generated by Grobner bases. We prove that any graph can be oriented such that its toric ideal is a complete intersection with a universal Grobner basis determined by the cycles. It turns out that bipartite ring graphs are exactly the bipartite graphs that have complete intersection toric ideals for any orientation. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1016/j.disc.2009.03.020 | Discrete Mathematics |
Keywords | Field | DocType |
toric ideal,ring graph,oriented graph,complete intersection,grobner basis,bipartite graph | Permutation graph,Discrete mathematics,Combinatorics,Indifference graph,Robertson–Seymour theorem,Chordal graph,Cograph,Pathwidth,1-planar graph,Mathematics,Maximal independent set | Journal |
Volume | Issue | ISSN |
310 | 3 | Discrete Mathematics |
Citations | PageRank | References |
6 | 1.37 | 6 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Isidoro Gitler | 1 | 29 | 7.03 |
| Enrique Reyes | 2 | 21 | 4.56 |
| Rafael H. Villarreal | 3 | 75 | 15.69 |