Name
Abstract | ||
|---|---|---|
We characterize all pairs of graphs (G1,G2), for which the binomial edge ideal J(G1,G2) has linear relations. We show that J(G1,G2) has a linear resolution if and only if G1 and G2 are complete and one of them is just an edge. We also compute some of the graded Betti numbers of the binomial edge ideal of a pair of graphs with respect to some graphical terms. In particular, we show that for every pair of graphs (G1,G2) with girth (i.e. the length of a shortest cycle in the graph) greater than 3, beta(i,i+2)(J(G1,G2)) = 0, for all i. Moreover, we give a lower bound for the Castelnuovo-Mumford regularity of any binomial edge ideal JG1,G2 and hence the ideal of adjacent 2-minors of a generic matrix. We also obtain an upper bound for the regularity of J(G1,G2) , if G1 is complete and G2 is a closed graph. |
Year | Venue | Keywords |
|---|---|---|
2013 | ELECTRONIC JOURNAL OF COMBINATORICS | Binomial edge ideal of a pair of graphs,Linear resolutions,Linear relations,Castelnuovo-Mumford regularity |
Field | DocType | Volume |
Discrete mathematics,Graph,Betti number,Combinatorics,Matrix (mathematics),Upper and lower bounds,Binomial,Castelnuovo–Mumford regularity,Mathematics | Journal | 20.0 |
Issue | ISSN | Citations |
1.0 | 1077-8926 | 1 |
PageRank | References | Authors |
0.43 | 5 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Sara Saeedi Madani | 1 | 6 | 2.13 |
| Dariush Kiani | 2 | 26 | 5.86 |