We show that the Castelnuovo–Mumford regularity of the binomial edge ideal of a graph is bounded below by the length of its longest induced path and bounded above by the number of its vertices.

We consider a class of graphs G such that the height of the edge ideal I(G) is half of the number ♯V (G) of the vertices. We give Cohen-Macaulay criteria for such graphs.

We study the Betti numbers of binomial edge ideal associated to some classes of graphs with large Castelnuovo-Mumford regularity. As an application we give several lower bounds of the Castelnuovo-Mumford regularity of arbitrary graphs depending on induced subgraphs.

Let I(G) be the edge ideal associated to a simple graph G. We study the graded Betti numbers that appear in the linear strand of the minimal free resolution of I(G).

In an ideal world, rise and fall times would be infinitely fast and every edge of a digital stream would consistently fall the exact same time away from the last. The end result would be no jitter, no wiggling, and no eyes diagrams that suffer from being closed or close to closed. Unfortunately it is not a perfect world, and what once was conceived as an infinitely fast edge, becomes slower as ...

For a bipartite graph G we are able to characterize the complete intersection property of the edge subring in terms of the multiplicity and we give optimal bounds for this number. We give a method to obtain a regular sequence for the atomic ideal of G, when G is embedded on an orientable surface. We also give a graph theoretical condition for the edge subring associated with G to be Gorenstein....

An old question of T. Jech and K. Prikry asks if an existence of a precipitous ideal implies necessary existence of a normal precipitous ideal. The aim of the paper is to prove some results in the positive direction. Thus, it is shown that under some mild assumptions, an existence of a precipitous ideal over א1 implies an existence of a normal precipitous ideal over א1 once a Cohen subset is ad...

the rings considered in this article are commutative with identity $1neq 0$. by a proper ideal of a ring $r$,  we mean an ideal $i$ of $r$ such that $ineq r$.  we say that a proper ideal $i$ of a ring $r$ is a  maximal non-prime ideal if $i$ is not a prime ideal of $r$ but any proper ideal $a$ of $r$ with $ isubseteq a$ and $ineq a$ is a prime ideal. that is, among all the proper ideals of $r$,...

We estimate the accuracy of a 3D range scanner in terms of its spatial frequency response. We determine a scanner’s modulation transfer function (MTF) in order to measure its frequency response. A slanted edge is scanned from which we derive a superresolution edge profile. Its Fourier transform is compared to the Fourier transform of an ideal edge in order to determine the MTF of the device. Th...