Results 11 to 20 of about 1,161,259 (282)
Koszul binomial edge ideals [PDF]
, 2013 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. Conca +16 more
core +2 more sources
Le Matematiche, 2012 We compute the Betti numbers for all the powers of initial and final lexsegment edge ideals. For the powers of the edge ideal of an anti–d−path, we prove that they have linear quotients and we characterize the normally torsion–free ideals. We determine a
Carmela Ferrò +2 more
doaj +3 more sources
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.
openaire +3 more sources
EDGE IDEALS OF WEIGHTED GRAPHS [PDF]
Journal of Algebra and Its Applications, 2013 We study weighted graphs and their "edge ideals" which are ideals in polynomial rings that are defined in terms of the graphs. We provide combinatorial descriptions of m-irreducible decompositions for the edge ideal of a weighted graph in terms of the combinatorics of "weighted vertex covers". We use these, for instance, to say when these ideals are m-
Paulsen, Chelsey, Sather-Wagstaff, Sean
openaire +3 more sources
Journal of Algebraic Combinatorics, 2012 The paper under review is inspired by the question of for which graphs do all powers of the edge ideals have linear resolutions. It is known (cf. \textit{D. Eisenbud} et al., [Compos. Math. 141, No. 6, 1460--1478 (2005; Zbl 1086.14044)] and \textit{H.T. Hà} and \textit{A. Van Tuyl} [J. Algebra 309, No. 1, 405--425 (2007; Zbl 1151.13017)]) that the edge
Nevo, Eran, Peeva, Irena
openaire +1 more source
Sequentially Cohen-Macaulay edge ideals [PDF]
Proceedings of the American Mathematical Society, 2007 Let G be a simple undirected graph on n vertices, and let I(G) \subseteq R = k[x_1,...,x_n] denote its associated edge ideal. We show that all chordal graphs G are sequentially Cohen-Macaulay; our proof depends upon showing that the Alexander dual of I(G) is componentwise linear.
Francisco, Christopher A. +1 more
openaire +2 more sources
Comparing powers of edge ideals [PDF]
Journal of Algebra and Its Applications, 2019 Given a nontrivial homogeneous ideal [Formula: see text], a problem of great recent interest has been the comparison of the [Formula: see text]th ordinary power of [Formula: see text] and the [Formula: see text]th symbolic power [Formula: see text]. This comparison has been undertaken directly via an exploration of which exponents [Formula: see text ...
Janssen, Mike +2 more
openaire +2 more sources
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.
Kiani, Dariush, Saeedi, Sara
openaire +2 more sources
Licci binomial edge ideals [PDF]
Journal of Combinatorial Theory, Series A, 2020 We give a complete characterization of graphs whose binomial edge ideal is licci. An important tool is a new general upper bound for the regularity of binomial edge ideals.
Ene V., Rinaldo G., Terai N.
openaire +3 more sources
Cohen-Macaulay binomial edge ideals [PDF]
Nagoya Mathematical Journal, 2011 AbstractWe 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
openaire +4 more sources