On vanishing patterns in j-strands of edge ideals

Abed Abedelfatah; Eran Nevo

doi:10.1007/s10801-017-0747-5

A proof for a conjecture on the regularity of binomial edge ideals

Journal of Combinatorial Theory Series A ◽

10.1016/j.jcta.2021.105432 ◽

2021 ◽

Vol 180 ◽

pp. 105432

Author(s):

Mohammad Rouzbahani Malayeri ◽

Sara Saeedi Madani ◽

Dariush Kiani

Keyword(s):

Edge Ideals

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Stanley depth of edge ideals

Studia Scientiarum Mathematicarum Hungarica ◽

10.1556/sscmath.49.2012.4.1223 ◽

2012 ◽

Vol 49 (4) ◽

pp. 501-508 ◽

Cited By ~ 1

Author(s):

Muhammad Ishaq ◽

Muhammad Qureshi

Keyword(s):

Complete Graph ◽

Upper Bound ◽

Edge Ideal ◽

Stanley Depth ◽

Edge Ideals

We give an upper bound for the Stanley depth of the edge ideal I of a k-partite complete graph and show that Stanley’s conjecture holds for I. Also we give an upper bound for the Stanley depth of the edge ideal of a s-uniform complete bipartite hypergraph.

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Gorenstein binomial edge ideals

Mathematische Nachrichten ◽

10.1002/mana.201900251 ◽

2021 ◽

Author(s):

René González‐Martínez

Keyword(s):

Edge Ideals

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Comparing powers of edge ideals

Journal of Algebra and Its Applications ◽

10.1142/s0219498819501846 ◽

2019 ◽

Vol 18 (10) ◽

pp. 1950184 ◽

Cited By ~ 1

Author(s):

Mike Janssen ◽

Thomas Kamp ◽

Jason Vander Woude

Keyword(s):

Symbolic Power ◽

Edge Ideal ◽

Homogeneous Ideal ◽

Edge Ideals ◽

Ideal Formula ◽

Number Of Generators ◽

Recent Interest ◽

Odd Cycle ◽

Ordinary Power

Given a nontrivial homogeneous ideal [Formula: see text], a problem of great recent interest has been the comparison of the [Formula: see text]th ordinary power of [Formula: see text] and the [Formula: see text]th symbolic power [Formula: see text]. This comparison has been undertaken directly via an exploration of which exponents [Formula: see text] and [Formula: see text] guarantee the subset containment [Formula: see text] and asymptotically via a computation of the resurgence [Formula: see text], a number for which any [Formula: see text] guarantees [Formula: see text]. Recently, a third quantity, the symbolic defect, was introduced; as [Formula: see text], the symbolic defect is the minimal number of generators required to add to [Formula: see text] in order to get [Formula: see text]. We consider these various means of comparison when [Formula: see text] is the edge ideal of certain graphs by describing an ideal [Formula: see text] for which [Formula: see text]. When [Formula: see text] is the edge ideal of an odd cycle, our description of the structure of [Formula: see text] yields solutions to both the direct and asymptotic containment questions, as well as a partial computation of the sequence of symbolic defects.

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The arithmetical rank of the edge ideals of cactus graphs

Communications in Algebra ◽

10.1080/00927872.2017.1310873 ◽

2017 ◽

Vol 45 (12) ◽

pp. 5407-5419

Author(s):

Margherita Barile ◽

Antonio Macchia

Keyword(s):

Edge Ideals ◽

Arithmetical Rank ◽

Cactus Graphs

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Edge ideals of clique clutters of comparability graphs and the normality of monomial ideals

MATHEMATICA SCANDINAVICA ◽

10.7146/math.scand.a-15126 ◽

2010 ◽

Vol 106 (1) ◽

pp. 88 ◽

Cited By ~ 4

Author(s):

Luis A. Dupont ◽

Rafael H. Villarreal

Keyword(s):

Monomial Ideal ◽

Lattice Points ◽

Edge Ideal ◽

Comparability Graph ◽

Decomposition Property ◽

Edge Ideals ◽

Finite Poset ◽

Integer Decomposition Property ◽

Torsion Free ◽

Min Cut

The normality of a monomial ideal is expressed in terms of lattice points of blocking polyhedra and the integer decomposition property. For edge ideals of clutters this property characterizes normality. Let $G$ be the comparability graph of a finite poset. If $\mathrm{cl}(G)$ is the clutter of maximal cliques of $G$, we prove that $\mathrm{cl}(G)$ satisfies the max-flow min-cut property and that its edge ideal is normally torsion free. Then we prove that edge ideals of complete admissible uniform clutters are normally torsion free.

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