Results 21 to 30 of about 38,270 (230)
Construction of Cohen–Macaulay Binomial Edge Ideals [PDF]
Communications in Algebra, 2013 We discuss algebraic and homological properties of binomial edge ideals associated to graphs which are obtained by gluing of subgraphs and the formation of cones.
Rauf A., RINALDO, GIANCARLO
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Binomial edge ideals of cographs
Revista de la Unión Matemática Argentina, 2022 We determine the Castelnuovo-Mumford regularity of binomial edge ideals of complement reducible graphs (cographs). For cographs with $n$ vertices the maximum regularity grows as $2n/3$. We also bound the regularity by graph theoretic invariants and construct a family of counterexamples to a conjecture of Hibi and Matsuda.
Kahle, Thomas, Krüsemann, Jonas
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Binomial edge ideals of Clutters
, 2021 In this paper, we introduce the notion of binomial edge ideals of a clutter and obtain results similar to those obtained for graphs by Rauf \& Rinaldo in \cite{raufrin}. We also answer a question posed in their paper.
Saha, Kamalesh, Sengupta, Indranath
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$$(S_2)$$-condition and Cohen–Macaulay binomial edge ideals
Journal of Algebraic Combinatorics, 2022 AbstractWe describe the simplicial complex $$\Delta $$ Δ such that the initial ideal of the binomial edge ideal $$J_\textrm{G}$$ J G of G is the Stanley-Reisner ideal of $$\Delta $$ Δ .
Lerda, A +3 more
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Binomial edge ideals of small depth [PDF]
Journal of Algebra, 2021 Let $G$ be a graph on $[n]$ and $J_G$ be the binomial edge ideal of $G$ in the polynomial ring $S=\mathbb{K}[x_1,\ldots,x_n,y_1,\ldots,y_n]$. In this paper we investigate some topological properties of a poset associated to the minimal primary decomposition of $J_G$. We show that this poset admits some specific subposets which are contractible. This in
Malayeri, Mohammad Rouzbahani +2 more
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Graph connectivity and binomial edge ideals
Proceedings of the American Mathematical Society, 2016 We relate homological properties of a binomial edge ideal $\mathcal{J}_G$ to invariants that measure the connectivity of a simple graph $G$. Specifically, we show if $R/\mathcal{J}_G$ is a Cohen-Macaulay ring, then graph toughness of $G$ is exactly $\frac{1}{2}$.
Banerjee, Arindam +1 more
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d-Sequence edge binomials, and regularity of powers of binomial edge ideals of trees
Journal of Algebra and Its Applications, 2023 In this paper, we provide the necessary and sufficient conditions for the edge binomials of the tree forming a [Formula: see text]-sequence in terms of the degree sequence notion of a graph. We study the regularity of powers of the binomial edge ideals of trees generated by [Formula: see text]-sequence edge binomials.
Marie Amalore Nambi, Neeraj Kumar
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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 +2 more
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Generalized binomial edge ideals
Advances in Applied Mathematics, 2013 This paper studies a class of binomial ideals associated to graphs with finite vertex sets. They generalize the binomial edge ideals, and they arise in the study of conditional independence ideals. A Gr bner basis can be computed by studying paths in the graph.
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Regularity of parity binomial edge ideals [PDF]
Proceedings of the American Mathematical Society, 2021 10 pages, Suggestions and comments are welcome.
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