Bounding Betti Numbers of Bipartite Graph Ideals
نویسنده
چکیده
We prove a conjectured lower bound of Nagel and Reiner on Betti numbers of edge ideals of bipartite graphs.
منابع مشابه
ar X iv : 0 80 7 . 21 85 v 1 [ m at h . A C ] 1 4 Ju l 2 00 8 SPLITTINGS OF MONOMIAL IDEALS
We provide some new conditions under which the graded Betti numbers of a mono-mial ideal can be computed in terms of the graded Betti numbers of smaller ideals, thus complementing Eliahou and Kervaire's splitting approach. As applications, we show that edge ideals of graphs are splittable, and we provide an iterative method for computing the Betti numbers of the cover ideals of Cohen-Macaulay b...
متن کاملSplittings of Monomial Ideals
We provide some new conditions under which the graded Betti numbers of a monomial ideal can be computed in terms of the graded Betti numbers of smaller ideals, thus complementing Eliahou and Kervaire’s splitting approach. As applications, we show that edge ideals of graphs are splittable, and we provide an iterative method for computing the Betti numbers of the cover ideals of Cohen-Macaulay bi...
متن کاملExtremal Betti Numbers of Some Classes of Binomial Edge Ideals
Let G be a simple graph on the vertex set [n] with edge set E(G) and let S be the polynomial ring K[x1, . . . , xn, y1, . . . , yn] in 2n variables endowed with the lexicographic order induced by x1 > · · · > xn > y1 > · · · > yn. The binomial edge ideal JG ⊂ S associated with G is generated by all the binomials fij = xiyj−xjyi with {i, j} ∈ E(G). The binomial edge ideals were introduced in [5]...
متن کاملOn a special class of Stanley-Reisner ideals
For an $n$-gon with vertices at points $1,2,cdots,n$, the Betti numbers of its suspension, the simplicial complex that involves two more vertices $n+1$ and $n+2$, is known. In this paper, with a constructive and simple proof, wegeneralize this result to find the minimal free resolution and Betti numbers of the $S$-module $S/I$ where $S=K[x_{1},cdots, x_{n}]$ and $I$ is the associated ideal to ...
متن کاملBounding cochordal cover number of graphs via vertex stretching
It is shown that when a special vertex stretching is applied to a graph, the cochordal cover number of the graph increases exactly by one, as it happens to its induced matching number and (Castelnuovo-Mumford) regularity. As a consequence, it is shown that the induced matching number and cochordal cover number of a special vertex stretching of a graph G are equal provided G is well-covered bipa...
متن کامل