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Cohen-Macaulay binomial edge ideals [PDF]
Nagoya Mathematical Journal, 2011 We study the depth of classes of binomial edge ideals and classify all closed graphs whose binomial edge ideal is Cohen--Macaulay.Comment: 9 ...
Ene, Viviana +2 more
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Smoothness in Binomial Edge Ideals [PDF]
Mathematics, 2016 In this paper we study some geometric properties of the algebraic set associated to the binomial edge ideal of a graph. We study the singularity and smoothness of the algebraic set associated to the binomial edge ideal of a graph. Some of these algebraic
Hamid Damadi, Farhad Rahmati
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Binomial edge ideals of bipartite graphs [PDF]
European Journal of Combinatorics, 2017 Binomial edge ideals are a noteworthy class of binomial ideals that can be associated with graphs, generalizing the ideals of 2-minors. For bipartite graphs we prove the converse of Hartshorne’s Connectedness Theorem, according to which if an ideal is ...
Bolognini, Davide +2 more
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The regularity of binomial edge ideals of graphs [PDF]
AUT Journal of Mathematics and Computing, 2020 In this paper, we study the Castelnuovo-Mumford regularity and the graded Betti numbers of the binomial edge ideals of some classes of graphs. Our special attention is devoted to a conjecture which asserts that the number of maximal cliques of a graph ...
Sara Saeedi Madani, Dariush Kiani
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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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Bayesian Verification Scheme for Software Reliability Based on Staged Growth Test Information [PDF]
Jisuanji kexueThe prior distribution determination methods of existing Bayesian schemes are relatively conservative and ideal for processing software reliability phased growth testing information.In this article,an edge distribution model for the software success ...
WANG Yuzhuo, LIU Haitao, YUAN Haojie, ZHAI Yali, ZHANG Zhihua
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Toric algebra of hypergraphs [PDF]
, 2013 The edges of any hypergraph parametrize a monomial algebra called the edge subring of the hypergraph. We study presentation ideals of these edge subrings, and describe their generators in terms of balanced walks on hypergraphs.
Petrović, Sonja, Stasi, Despina
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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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Algebraic properties of the binomial edge ideal of a complete bipartite graph
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2014 Let JG denote the binomial edge ideal of a connected undirected graph on n vertices. This is the ideal generated by the binomials xiyj − xjyi, 1 ≤ i < j≤ n, in the polynomial ring S = K[x1, . . . , xn, y1, . . . , yn] where {i, j} is an edge of G.
Schenzel Peter, Zafar Sohail
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Some Cohen-Macaulay and unmixed binomial edge ideals
, 2015 We study unmixed and Cohen-Macaulay properties of the binomial edge ideal of some classes of graphs. We compute the depth of the binomial edge ideal of a generalized block graph.
Kiani, Dariush, Madani, Sara Saeedi
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