In this paper we introduce the concept of clique disjoint edge sets in graphs. Then, for a
graph G, we define the invariant η (G) as the maximum size of a clique disjoint edge set in G …

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We study the regularity of binomial edge ideals. For a closed graph G we show that the
regularity of the binomial edge ideal coincides with the regularity of and can be expressed in …

We characterize all pairs of graphs $(G_1, G_2) $, for which the binomial edge ideal $ J_
{G_1, G_2} $ has linear relations. We show that $ J_ {G_1, G_2} $ has a linear resolution if …

We characterize all graphs whose binomial edge ideals have a linear resolution. Indeed, we
show that complete graphs are the only graphs with this property. We also compute some …

Let JG be the binomial edge ideal of a graph G. We characterize all graphs whose binomial
edge ideals, as well as their initial ideals, have regularity 3. Consequently we characterize …

We determine the Castelnuovo-Mumford regularity of binomial edge ideals of complement
reducible graphs (cographs). For cographs with $ n $ vertices the maximum regularity grows …

We prove that the regularity of binomial edge ideals of graphs obtained by gluing two graphs
at a free vertex is the sum of the regularity of individual graphs. As a consequence, we …

Let G be a finite simple graph and I(G) denote the corresponding edge ideal. In this paper,
we prove that, if G is a unicyclic graph, then, for all s≧1, the regularity of I(G)^s is exactly …

We prove two recent conjectures on some upper bounds for the Castelnuovo-Mumford
regularity of the binomial edge ideals of some different classes of graphs. We prove the …