Let G be a finite simple graph and I (G) denote the corresponding edge ideal. For all s ≥ 1
s≥ 1, we obtain upper bounds for reg (I (G)^ s) reg (I (G) s) for bipartite graphs. We then …

We survey recent studies on the Castelnuovo–Mumford regularity of edge ideals of graphs
and their powers. Our focus is on bounds and exact values of reg I (G) reg I (G) and the …

POWERS OF EDGE IDEALS OF REGULARITY THREE BIPARTITE GRAPHS 1. Introduction. Let
R = K[x1,...,xn] be the polynomial ring over af Page 1 JOURNAL OF COMMUTATIVE ALGEBRA …

Estimates are obtained for the degrees of minimal syzygies of quotient algebras of
polynomial rings. For a class that includes Koszul algebras in almost all characteristics …

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Let $ G $ be a finite simple graph and let $ I_G $ denote its associated toric ideal in the
polynomial ring $ R $. For each integer $ n\geq 2$, we completely determine all the possible …

For a simple graph G with edge ideal I (G), we study the N-graded Betti numbers in the linear
strand of the minimal free resolution of I (Γ (Z n)), where Γ (Z n) is the zero divisor graph of …

A Koszul algebra R is a N-graded K-algebra whose residue field K has a linear free
resolution as an R-module. We present various characterizations of Koszul algebras and …

In this paper, we study the conjecture of Kühnel and Lutz, who state that a combinatorial
triangulation of the product of two spheres\mathbb S^ i *\mathbb S^ j S i× S j with j ≥ ij≥ i is …

Fröberg's classical theorem about edge ideals with 2-linear resolution can be regarded as a
classification of graphs whose edge ideals have linearity defect zero. Extending his theorem …