Results 11 to 20 of about 27,934 (169)
Gorenstein binomial edge ideals [PDF]
Mathematische Nachrichten, 2021 AbstractWe classify connected graphs G whose binomial edge ideal is Gorenstein. In our proofs we use Frobenius type techniques and F‐pure thresholds.
exaly +5 more sources
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].
Rajib Sarkar
openalex +4 more sources
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
openaire +4 more sources
Combinatorics of Castelnuovo-Mumford Regularity of Binomial Edge Ideals [PDF]
Electronic Journal of Combinatorics, 2023 Since the introduction of binomial edge ideals by Herzog et al. and independently Ohtani, there has been significant interest in relating algebraic invariants of the binomial edge ideal with combinatorial invariants of the underlying graph. Here, we take
Adam LaClair
openalex +2 more sources
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
core +5 more sources
Binomial edge ideals of small depth [PDF]
Journal of Algebra, 2020 Let $G$ be a graph on $[n]$ and $J_G$ be the binomial edge ideal of $G$ in the polynomial ring $S=\mathbb{K}[x_1,\ldots,x_n,y_1,\ldots,y_n]$. In this paper we investigate some topological properties of a poset associated to the minimal primary decomposition of $J_G$. We show that this poset admits some specific subposets which are contractible. This in
Mohammad Rouzbahani Malayeri +2 more
openalex +5 more sources
Parity binomial edge ideals [PDF]
Journal of Algebraic Combinatorics, 2015 21 pages, 3 figures, v2: minor problem in proof of Lemma 2.4 corrected, construction of Gr\"obner basis in Section 3 corrected, Example 5.1 replaced by Remark 5.1, final version as in Journal of Algebraic Combinatorics, v3: footnote to Lemma 3.8 ...
Kahle, Thomas +2 more
openaire +4 more sources
Invariants of binomial edge ideals via linear programs [PDF]
Journal of Algebraic Combinatorics, 2023 We associate with every graph a linear program for packings of vertex disjoint paths. We show that the optimal primal and dual values of the corresponding integer program are the binomial grade and height of the binomial edge ideal of the graph.
Adam LaClair
openalex +2 more sources
The Castelnuovo-Mumford regularity of binomial edge ideals [PDF]
Journal of Combinatorial Theory, Series A, 2015 arXiv admin note: substantial text overlap with arXiv:1310 ...
Dariush Kiani, Sara Saeedi Madani
openalex +4 more sources
Binomial edge ideals and rational normal scrolls [PDF]
, 2014 Let $X$ be the Hankel matrix of size $2\times n$ and let $G$ be a closed graph on the vertex set $[n].$ We study the binomial ideal $I_G\subset K[x_1,\ldots,x_{n+1}]$ which is generated by all the $2$-minors of $X$ which correspond to the edges of $G ...
Faryal Chaudhry +2 more
openalex +4 more sources