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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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Sequentially Cohen-Macaulay binomial edge ideals of closed graphs [PDF]
, 2022 In this paper we provide a full combinatorial characterization of sequentially Cohen-Macaulay binomial edge ideals of closed graphs. In addition, we show that a binomial edge ideal of a closed graph is approximately Cohen-Macaulay if and only if it is ...
Ene, Viviana +2 more
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POWERS OF BINOMIAL EDGE IDEALS WITH QUADRATIC GRÖBNER BASES [PDF]
Nagoya Mathematical Journal, 2021 AbstractWe study powers of binomial edge ideals associated with closed and block graphs.
VIVIANA ENE +2 more
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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 generalized block graphs [PDF]
International Journal of Algebra and Computation, 2020 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 ...
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Hilbert function of binomial edge ideals
, 2014 In this paper the numerical invariants of the binomial edge ideal of a graph are ...
Mohammadi, Fatemeh +2 more
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Invariants of Binomial Edge Ideals via Linear Programs [PDF]
, 2023 We associate to every graph a linear program for packings of vertex disjoint paths. We show that the optimal primal and dual values of the corresponding integer program are the binomial grade and height of the binomial edge ideal of the graph.
LaClair, Adam
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Parity binomial edge ideals [PDF]
Journal of Algebraic Combinatorics, 2015 21 pages, 3 figures, v2: minor problem in proof of Lemma 2.4 corrected, construction of Gr\"obner basis in Section 3 corrected, Example 5.1 replaced by Remark 5.1, final version as in Journal of Algebraic Combinatorics, v3: footnote to Lemma 3.8 ...
Kahle, Thomas +2 more
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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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Cohen-Macaulay generalized binomial edge ideals
, 2023 Let $G$ be a simple graph on $n$ vertices and let $J_{G,m}$ be the generalized binomial edge ideal associated to $G$ in the polynomial ring $K[x_{ij}, 1\le i \le m, 1\le j \le n]$. We classify the Cohen-Macaulay generalized binomial edge ideals. Moreover
Crupi, Marilena +2 more
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