Results 11 to 20 of about 1,836,425 (146)
Binomial edge ideals of bipartite graphs [PDF]
European Journal of Combinatorics, 2018 We classify the bipartite graphs $G$ whose binomial edge ideal $J_G$ is Cohen-Macaulay. The connected components of such graphs can be obtained by gluing a finite number of basic blocks with two operations. In this context we prove the converse of a well-known result due to Hartshorne, showing that the Cohen-Macaulayness of these ideals is equivalent ...
Davide Bolognini +2 more
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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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Generalized binomial edge ideals [PDF]
Advances in Applied Mathematics, 2013 6 pages.
Rauh, Johannes, Johannes Rauh
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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).
Seccia, Lisa
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Binomial Edge Ideals of Graphs [PDF]
The Electronic Journal of Combinatorics, 2012 We characterize all graphs whose binomial edge ideals have a linear resolution. Indeed, we show that complete graphs are the only graphs with this property. We also compute some graded components of the first Betti number of the binomial edge ideal of a graph with respect to the graphical terms.
Dariush Kiani, Sara Saeedi Madani
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Binomial edge ideals of unicyclic graphs [PDF]
International Journal of Algebra and Computation, 2021 Let [Formula: see text] be a connected graph on the vertex set [Formula: see text]. Then [Formula: see text]. In this paper, we prove that if [Formula: see text] is a unicyclic graph, then the depth of [Formula: see text] is bounded below by [Formula: see text]. Also, we characterize [Formula: see text] with [Formula: see text] and [Formula: see text].
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On The Binomial Edge Ideal of a Pair of Graphs [PDF]
The Electronic Journal of Combinatorics, 2013 We characterize all pairs of graphs $(G_1,G_2)$, for which the binomial edge ideal $J_{G_1,G_2}$ has linear relations. We show that $J_{G_1,G_2}$ has a linear resolution if and only if $G_1$ and $G_2$ are complete and one of them is just an edge. We also compute some of the graded Betti numbers of the binomial edge ideal of a pair of graphs with ...
Sara Saeedi Madani, Dariush Kiani
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Cohen-Macaulay binomial edge ideals and accessible graphs [PDF]
, 2022 The 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
Strazzanti Francesco +2 more
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Recent results on homological properties of binomial edge ideal of graphs [PDF]
, 2023 In this article, we give a comprehensive survey of the recent progress of research on binomial edge ideal of a graph since ...
Das, Priya
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Koszul Binomial Edge Ideals [PDF]
, 2014 It is shown that if the binomial edge ideal of a graph $G$ defines a Koszul algebra, then $G$ must be chordal and claw free. A converse of this statement is proved for a class of chordal and claw free graphs.
Ene, Viviana +2 more
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