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Binomial Edge Ideals of Weakly Closed Graphs
International Mathematics Research Notices, 2022 Abstract Closed graphs have been characterized by Herzog et al. as the graphs whose binomial edge ideals have a quadratic Gröbner basis with respect to a diagonal term order. In this paper, we focus on a generalization of closed graphs, namely weakly closed graphs (or co-comparability graphs).
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The regularity of binomial edge ideals of graphs [PDF]
, 2013 We prove two recent conjectures on some upper bounds for the Castelnuovo-Mumford regularity of the binomial edge ideals of some different classes of graphs.
Dariush Kiani, Saeedi Madani, Sara
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Extremal Betti numbers of some classes of binomial edge ideals [PDF]
, 2013 Let $G$ be a cycle or a complete bipartite graph. We show that the binomial edge ideal $J_{G}$ and its initial ideal with respect to the lexicographic order have the same extremal Betti ...
Dokuyucu, Ahmet
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Minimal generators of toric ideals of graphs [PDF]
, 2010 Let $I_G$ be the toric ideal of a graph $G$. We characterize in graph theoretical terms the primitive, the minimal, the indispensable and the fundamental binomials of the toric ideal $I_G$
Reyes, Enrique +2 more
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Koszulness of binomial edge ideals
, 2010 10 pages, 1 figure The title has changed in: Binomial edge ideals with quadratic Gr\"obner ...
Crupi, Marilena, Rinaldo, Giancarlo
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Toricness of Binomial Edge Ideals
, 2012 Let G be a finite simple graph. In this paper we will show that the binomial edge ideal of G, JG is toric if and only if each connected component of G is complete and in this case it is the sum of toric ideal associated to bipartite complete graphs.
Saeedi, Mahdis +2 more
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Cohen-Macaulay generalized binomial edge ideals
, 2021 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 we study the unmixedness and classify the bipartite and power cycle unmixed ones.
Amata, Luca +2 more
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Powers of generalized binomial edge ideals of path graphs [PDF]
, 2023 Yi-Huang Shen, Guangjun Zhu
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Arithmetical rank and cohomological dimension of generalized binomial edge ideals [PDF]
, 2022 Anargyros Katsabekis
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Recent results on homological properties of binomial edge ideal of graphs [PDF]
, 2022 Das, Priya
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