‎A recent result due to Ha and Van Tuyl proved that the Castelnuovo-Mumford regularity of the quotient ring $R/I(G)$ is at most matching number of $G$‎, ‎denoted by match$(G)$‎. ‎In this paper‎, ‎we provide a generalization of this result for powers of edge ideals‎. ‎More precisely‎, ‎we show that for every graph $G$ and every $sgeq 1$‎, ‎$${rm reg}( R‎/ ‎I(G)^{s})leq (2s-1) |E(G)|^{s-1} {rm ma...

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...

Abstract In this paper we study ideals of points lying on rational normal curves defined in projective plane and 3-space. We give an explicit formula for the value Castelnuovo–Mumford regularity their ordinary powers. Moreover, compare m -th symbolic powers such order to show whenever defect is non-zero.

We define the concept of regularity for bigraded modules over a bigraded polynomial ring. In this setting we prove analogs of some of the classical results on m-regularity for graded modules over polynomial algebras.

We consider a set X of distinct points in the n-dimensional projective space over an algebraically closed field k. Let A denote the coordinate ring of X , and let ai(X) = dimk[Tor R i (A, k)]i+1. Green’s Strong Castelnuovo Lemma (SCL) shows that if the points are in general position, then an−1(X) 6= 0 if and only if the points are on a rational normal curve. Cavaliere, Rossi and Valla conjectur...