Gorenstein binomial edge ideals
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DOI: 10.1002/mana.201900251
Abstract: We classify connected graphs G whose binomial edge ideal is Gorenstein. The proof uses methods in prime characteristic. read more here.
Keywords: binomial edge; gorenstein binomial; edge; edge ideals ... See more keywords
Binomial edge ideals and bounds for their regularity
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DOI: 10.1007/s10801-020-00939-2
Abstract: Let G be a simple graph on n vertices and $$J_G$$ denote the corresponding binomial edge ideal in $$S = K[x_1, \ldots , x_n, y_1, \ldots , y_n].$$ We prove that the Castelnuovo–Mumford regularity of… read more here.
Keywords: ideals bounds; edge; regularity binomial; binomial edge ... See more keywords
Regularity of Powers of Edge Ideals of Some Graphs
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DOI: 10.1007/s40306-017-0204-5
Abstract: Let Cn~$\tilde {C_{n}}$ be the graph by adding an ear to Cn and I=I(Cn~)$I=I(\tilde {C_{n}})$ be its edge ideal. In this paper, we prove that reg(Is)=2s+⌊n+13⌋−1$\operatorname {reg}(I^{s})=2s+\lfloor \frac {n+1}{3}\rfloor -1$ for all s ≥ 1.… read more here.
Keywords: frac rfloor; powers edge; regularity; lfloor frac ... See more keywords
Algebraic Properties of Edge Ideals and Cover Ideals of Unbalanced Crown Graphs
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DOI: 10.1007/s41980-021-00560-4
Abstract: In this paper, we introduce the unbalanced crown graphs $${\mathcal {C}}_{m,n}$$ , and compute all graded Betti numbers of edge ideals of these graphs in terms of associated numerical data. As a consequence, we determine… read more here.
Keywords: edge ideals; crown graphs; algebraic properties; unbalanced crown ... See more keywords
Regularity of powers of quadratic sequences with applications to binomial ideals
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DOI: 10.1016/j.jalgebra.2020.08.004
Abstract: Abstract In this article, we obtain an upper bound for the Castelnuovo-Mumford regularity of powers of an ideal generated by a homogeneous quadratic sequence in a polynomial ring in terms of the regularity of its… read more here.
Keywords: edge ideals; binomial ideals; regularity; binomial edge ... See more keywords
ON THE DEPTH OF SYMBOLIC POWERS OF EDGE IDEALS OF GRAPHS
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DOI: 10.1017/nmj.2020.27
Abstract: Abstract Assume that G is a graph with edge ideal $I(G)$ and star packing number $\alpha _2(G)$ . We denote the sth symbolic power of $I(G)$ by $I(G)^{(s)}$ . It is shown that the inequality… read more here.
Keywords: edge ideals; symbolic powers; powers edge; ideals graphs ... See more keywords
Powers of edge ideals with linear resolutions
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DOI: 10.1080/00927872.2018.1430810
Abstract: ABSTRACT We show that if G is a gap-free and diamond-free graph, then I(G)s has a linear minimal free resolution for every s≥2. read more here.
Keywords: ideals linear; powers edge; linear resolutions; edge ideals ... See more keywords
Cohen-Macaulay edge-weighted edge ideals of very well-covered graphs
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DOI: 10.1080/00927872.2021.1917590
Abstract: Abstract We characterize unmixed and Cohen-Macaulay edge-weighted edge ideals of very well-covered graphs. We also provide examples of oriented graphs that have unmixed and non-Cohen-Macaulay vertex-weighted edge ideals, while the edge ideal of their underlying… read more here.
Keywords: cohen macaulay; edge ideals; edge; weighted edge ... See more keywords
Associated primes of powers of edge ideals and ear decompositions of graphs
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DOI: 10.1090/tran/7662
Abstract: In this paper, we give a complete description of the associated primes of every power of the edge ideal in terms of generalized ear decompositions of the graph. This result establishes a surprising relationship between… read more here.
Keywords: ear decompositions; powers edge; associated primes; ideals ear ... See more keywords
The powers of unmixed bipartite edge ideals
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DOI: 10.1142/s0219498819502098
Abstract: In this paper, we study the depth and the Castelnuovo–Mumford regularity of the powers of edge ideals which are unmixed and whose underlying graphs are bipartite. In particular, we prove that the depth of the… read more here.
Keywords: edge ideals; regularity; unmixed bipartite; powers edge ... See more keywords
Krull dimension and regularity of binomial edge ideals of block graphs
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DOI: 10.1142/s0219498820501339
Abstract: We give a lower bound for the Castelnuovo-Mumford regularity of binomial edge ideals of block graphs by computing the two distinguished extremal Betti numbers of a new family of block graphs, called flower graphs. Moreover,… read more here.
Keywords: edge ideals; ideals block; block graphs; regularity ... See more keywords