Results 41 to 50 of about 27,934 (169)
Regularity and h-polynomials of Binomial Edge Ideals [PDF]
Acta Mathematica Vietnamica, 2021 6 pages. Conjecture 0.1 has been deleted.
Hibi, Takayuki, Matsuda, Kazunori
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Binomial edge ideals of regularity 3 [PDF]
Journal of Algebra, 2018 Let $J_G$ be the binomial edge ideal of a graph $G$. We characterize all graphs whose binomial edge ideals, as well as their initial ideals, have regularity $3$. Consequently we characterize all graphs $G$ such that $J_G$ is extremal Gorenstein. Indeed, these characterizations are consequences of an explicit formula we obtain for the regularity of the ...
Saeedi Madani, Sara, Kiani, Dariush
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Binomial Edge Ideals with Quadratic Gröbner Bases [PDF]
The Electronic Journal of Combinatorics, 2011 We prove that a binomial edge ideal of a graph $G$ has a quadratic Gröbner basis with respect to some term order if and only if the graph $G$ is closed with respect to a given labelling of the vertices. We also state some criteria for the closedness of a graph $G$ that do not depend on the labelling of its vertex set.
CRUPI, Marilena, RINALDO, GIANCARLO
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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 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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On the binomial edge ideals of block graphs
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2016 We find a class of block graphs whose binomial edge ideals have minimal regularity. As a consequence, we characterize the trees whose binomial edge ideals have minimal regularity.
Chaudhry Faryal +2 more
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Toric ideals and diagonal 2-minors [PDF]
, 2016 Let $G$ be a simple graph on the vertex set $\{1,\ldots,n\}$ with $m$ edges. An algebraic object attached to $G$ is the ideal $P_{G}$ generated by diagonal 2-minors of an $n \times n$ matrix of variables.
Katsabekis, Anargyros
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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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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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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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