Results 21 to 30 of about 27,934 (169)

Regularity of Initial Ideal of Binomial Edge Ideals in Degree 2 and Their Powers

Contemporary Mathematics
In this paper, we study the Castelnuovo-Mumford regularity of the initial ideal of binomial edge ideals in degree 2 ...
Bakhtyar Mahmood Rahim, Hero Saremi, Mudhafar Hama   +2 more
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Some Cohen-Macaulay and unmixed binomial edge ideals

Communications in Algebra, 2015
We study unmixed and Cohen-Macaulay properties of the binomial edge ideal of some classes of graphs. We compute the depth of the binomial edge ideal of a generalized block graph.
Kiani, Dariush, Madani, Sara Saeedi
core   +3 more sources

On the symbolic $F$-splitness of binomial edge ideals [PDF]

Journal of Pure and Applied Algebra
We study the symbolic $F$-splitness of families of binomial edge ideals. We also study the strong $F$-regularity of the symbolic blowup algebras of families of binomial edge ideals.
Pedro Ramírez-Moreno
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Multidegrees of binomial edge ideals

Communications in Algebra
We prove how to calculate the multidegree of a binomial edge ideal based on combinatorial properties of the underlying graph. In particular, we study the collection of subsets of vertices whose prime ideals have minimum codimension.
Jacob Cooper, Ethan Leventhal
semanticscholar   +3 more sources

Cohen–Macaulay binomial edge ideals and accessible graphs [PDF]

Journal of Algebraic Combinatorics, 2021
AbstractThe cut sets of a graph are special sets of vertices whose removal disconnects the graph. They are fundamental in the study of binomial edge ideals, since they encode their minimal primary decomposition. We introduce the class of accessible graphs as the graphs with unmixed binomial edge ideal and whose cut sets form an accessible set system ...
Davide Bolognini, Antonio Macchia, Francesco Strazzanti   +2 more
openaire   +5 more sources

A combinatorial characterization of S2 binomial edge ideals

European journal of combinatorics (Print), 2023
Several algebraic properties of a binomial edge ideal $J_G$ can be interpreted in terms of combinatorial properties of its associated graph $G$. In particular, the so-called cut sets of a graph $G$, special sets of vertices that disconnect $G$ in a ...
D. Bolognini, Antonio Macchia, Giancarlo Rinaldo, Francesco Strazzanti   +3 more
semanticscholar   +4 more sources

Binomial Edge Ideal of Generalized block graph [PDF]

International Journal of Algebra and Computation, 2019
We classify generalized block graphs whose binomial edge ideals admit a unique extremal Betti number. We prove that the Castelnuovo–Mumford regularity of binomial edge ideals of generalized block graphs is bounded below by [Formula: see text], where [Formula: see text] is the number of minimal cut sets of the graph [Formula: see text] and obtain an ...
Arvind Kumar
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F-Purity of Binomial Edge Ideals

Journal of the London Mathematical Society
In 2012, Matsuda introduced the class of weakly closed graphs and investigated when binomial edge ideals are F‐pure. He proved that weakly closed binomial edge ideals are F‐pure whenever the base field has positive characteristic. He conjectured that: (i)
Adam LaClair, Jason McCullough
openalex   +2 more sources

Regularity bounds for binomial edge ideals [PDF]

Journal of Commutative Algebra, 2012
We show that the Castelnuovo-Mumford regularity of the binomial edge ideal of a graph is bounded below by the length of its longest induced path and bounded above by the number of its vertices.
Kazunori Matsuda, Satoshi Murai
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Binomial edge ideals of crown graphs

Journal of Algebraic Combinatorics
In this article, we explore the class of graphs for which the projective dimension of the quotient of the binomial edge ideals matches the big height of that ideal.
Arvind Kumar, Joshua Pomeroy, L. Tran
semanticscholar   +3 more sources