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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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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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The $\mathrm{v}$-Number of Binomial Edge Ideals [PDF]
, 2023 The invariant $\mathrm{v}$-number was introduced very recently in the study of Reed-Muller-type codes. Jaramillo and Villarreal (J Combin. Theory Ser. A 177:105310, 2021) initiated the study of the $\mathrm{v}$-number of edge ideals.
Sengupta, Indranath +2 more
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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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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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Level and pseudo-Gorenstein binomial edge ideals
, 2023 We prove that level binomial edge ideals with regularity 2 and pseudo-Gorenstein binomial edge ideals with regularity 3 are cones, and we describe them completely. Also, we characterize level and pseudo-Gorenstein binomial edge ideals of bipartite graphs.
Rinaldo, Giancarlo +3 more
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On the Symbolic Powers of Binomial Edge Ideals [PDF]
, 2020 We show that under some conditions, if the initial ideal in ...
Ene, Viviana, Herzog, Jürgen
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A combinatorial characterization of $S_2$ binomial edge ideals
Eur. J. Comb., 2023 Several algebraic properties of a binomial edge ideal $J_G$ can be interpreted in terms of combinatorial properties of its associated graph $G$. In particular, the so-called cut sets of a graph $G$, special sets of vertices that disconnect $G$ in a minimal way, play an important role since they are in bijection with the minimal prime ideals of $J_G ...
Bolognini D. +3 more
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Hilbert series of binomial edge ideals [PDF]
Communications in Algebra, 2019 13 pages, 2 images, typo error corrected, Accepted in Comm ...
Arvind Kumar, Rajib Sarkar
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Cohen-Macaulay binomial edge ideals [PDF]
Nagoya Mathematical Journal, 2011 Abstract We study the depth of classes of binomial edge ideals and classify all closed graphs whose binomial edge ideal is Cohen-Macaulay.
Ene, Viviana +2 more
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