… proofs of some formulas for the regularity. If R= IC/is sequentially Cohen–Macaulay, we present
a formula for the regularity of the ideal … primes of powers of edge ideals, and show that for …

… size of a clique disjoint edge set in G. We show that the regularity of the binomial edge ideal
of G is … This, in particular, settles a conjecture on the regularity of binomial edge ideals in full …

… that the Castelnuovo–Mumford regularity is subadditive on binomial edge ideals. … is the
associated binomial edge ideal. We prove a special case of this conjecture which strengthens the …

… We end with a conjecture about the persistence of associated primes for cover … Furthermore,
we prove that the edge and cover ideals are dual to each other with respect to Alexander …

… We are then able to use this decomposition to resolve [9, Conjecture 15], compute ρ(I(C2n+1))
in … Before stating and proving the lemma, we illustrate the process with an example. …

… corresponding edge ideal. … prove a weaker version of a conjecture by Alilooee, Banerjee,
Beyarslan and Hà on an upper bound for the regularity of I ( G ) q and we prove the conjectured …

… of edge ideals of graphs G in the case that G is a chordal graph. Here we provide a short
proof of … In this section we also answer in the affirmative a suggestion/conjecture made in [15] …

… patterns in the Betti table of edge ideals I over any fixed field. … to establish the subadditivity
conjecture for edge ideals, \(t_{a+b}… In this section we prove Theorem 1.3. First, we treat the …

… In this section, we prove that the initial ideal of binomial edge ideals of trees are normally
torsionfree. Additionally, we show that the symbolic powers and ordinary powers of binomial …

… prove Saeedi Madani–Kiani conjecture for some classes of non-chordal graphs. We prove
Conjecture … Then, we prove Conjecture 1.1 for semi-block graphs (see Sect. 3 for the definition…