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 …

Squarefree powers of edge ideals are intimately related to matchings of the underlying
graph. In this paper, we give bounds for the regularity of squarefree powers of edge ideals …

Let G be a finite simple graph and I (G) denote the corresponding edge ideal. In this paper,
we obtain upper bounds for the Castelnuovo-Mumford regularity of I (G) q in terms of certain …

A Cameron-Walker graph is a graph for which the matching number and the induced
matching number are the same. Assume that G is a Cameron-Walker graph with edge ideal I …

Assume that G is a graph with edge ideal I (G) and matching number match (G). For every
integer s≥ 1, we denote the s-th squarefree power of I (G) by I (G)[s]. It is shown that for …

Let $ I (G)^{[k]} $ denote the $ k $ th squarefree power of the edge ideal of $ G $. When $ G $
is a forest, we provide a sharp upper bound for the regularity of $ I (G)^{[k]} $ in terms of the …

Assume that $ G $ is a graph with edge ideal $ I (G) $. For every integer $ s\geq 1$, we
denote the squarefree part of the $ s $-th symbolic power of $ I (G) $ by $ I (G)^{\{s\}} $. We …

We study the independence complexes of families of well-covered circulant graphs
discovered by Boros–Gurvich–Milanič, Brown–Hoshino, and Moussi. Because these graphs …

Let $ G $ be a finite simple connected graph on $[n] $ and\[R= K [x_1,\ldots, x_n]\] the
polynomial ring in $ n $ variables over a field $ K $. The edge ideal of $ G $ is the ideal $ I …

Let G be a simple graph and let β (G) β (G) be the matching number of G. It is well-known
that\, reg\, I (G)\leqslant β (G)+ 1 reg I (G)⩽ β (G)+ 1. In this paper we show that\, reg\, I (G)= β …