Linear polynomials for the regularity of powers of edge ideals of very well-covered graphs

2021 ◽  
Vol 13 (1) ◽  
Author(s):  
A. V. Jayanthan ◽  
S. Selvaraja
Keyword(s):  
Edge Ideals ◽  
Linear Polynomials

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

2021 ◽  
Vol 180 ◽  
pp. 105432
Author(s):  
Mohammad Rouzbahani Malayeri ◽  
Sara Saeedi Madani ◽  
Dariush Kiani
Keyword(s):  
Edge Ideals

scholarly journals On vanishing patterns in j-strands of edge ideals

2017 ◽  
Vol 46 (2) ◽  
pp. 287-295 ◽  
Author(s):  
Abed Abedelfatah ◽  
Eran Nevo
Keyword(s):  
Edge Ideals

scholarly journals Stanley depth of edge ideals

2012 ◽  
Vol 49 (4) ◽  
pp. 501-508 ◽  
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.

scholarly journals Gorenstein binomial edge ideals

2021 ◽  
Author(s):  
René González‐Martínez
Keyword(s):  
Edge Ideals

scholarly journals Comparing powers of edge ideals

2019 ◽  
Vol 18 (10) ◽  
pp. 1950184 ◽  
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.

The arithmetical rank of the edge ideals of cactus graphs

2017 ◽  
Vol 45 (12) ◽  
pp. 5407-5419
Author(s):  
Margherita Barile ◽  
Antonio Macchia
Keyword(s):  
Edge Ideals ◽  
Arithmetical Rank ◽  
Cactus Graphs

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

2010 ◽  
Vol 106 (1) ◽  
pp. 88 ◽  
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.

scholarly journals NP-complete problems for systems of divisibilities of values of linear polynomials

2017 ◽  
Vol 4(62) (2) ◽  
pp. 236-246
Author(s):  
Nikolay K. Kosovskii ◽  
◽  
Tatiana M. Kosovskaya ◽  
Nikolay N. Kosovskii ◽  
Mikhail R. Starchak ◽  
...  
Keyword(s):  
Complete Problems ◽  
Np Complete ◽  
Linear Polynomials
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