Results 41 to 50 of about 1,161,259 (282)

Cohen–Macaulayness for symbolic power ideals of edge ideals

Journal of Algebra, 2011
Let $S = K[x_1,..., x_n]$ be a polynomial ring over a field $K$. Let $I(G) \subseteq S$ denote the edge ideal of a graph $G$. We show that the $\ell$th symbolic power $I(G)^{(\ell)}$ is a Cohen-Macaulay ideal (i.e., $S/I(G)^{(\ell)}$ is Cohen-Macaulay) for some integer $\ell \ge 3$ if and only if $G$ is a disjoint union of finitely many complete graphs.
RINALDO, GIANCARLO, Ken Ichi Yoshida, Naoki Terai   +2 more
openaire   +4 more sources

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
core   +1 more source

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
core   +1 more source

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
openaire   +2 more sources

DEPTH AND STANLEY DEPTH OF THE EDGE IDEALS OF SOME m-LINE GRAPHS AND m-CYCLIC GRAPHS WITH A COMMON VERTEX [PDF]

Romanian Journal of Mathematics and Computer Science, 2015
We give some precise formulas for the depth of the quotient rings of the edge ideals associated to a graph consisting, either of the union of some line graphs L_{3r_1}},...,L_{3r_{k_1}}, L_{3s_1+1}, ...,L_{3s_{k_2}+1} and L_{3t_1+2},...,L_{3t_{k_3}+2} or
GUANGJUN ZHU
doaj  

Symbolic powers of monomial ideals and Cohen-Macaulay vertex-weighted digraphs

, 2018
In this paper we study irreducible representations and symbolic Rees algebras of monomial ideals. Then we examine edge ideals associated to vertex-weighted oriented graphs.
A Simis, A Simis, A Simis, A Tuyl Van, AN Nejad, C Bahiano, Cesar Escobar, CHELSEY PAULSEN, Christopher A. Francisco, Cícero Carvalho, E Miller, F Harary, H Dao, H Matsumura, HT Hà, I Gitler, J Herzog, J Herzog, J Martínez-Bernal, Jorge Neves, Jürgen Herzog, LA Dupont, O Zariski, P Gimenez, RH Villarreal, S Goto, S Morey, Serkan Hoşten, Susan M. Cooper, V Crispin Quiñonez   +29 more
core   +1 more source

Algebraic invariants of edge ideals from strong products of paths and cycles

AIMS Mathematics
This paper investigates algebraic invariants of edge ideals associated with families of graphs constructed as the strong product of a path or cycle with the complete graph $ K_m $, namely $ \mathscr{P}_\gamma = P_\gamma \boxtimes K_m $ and $ \mathscr{C}_\
Ahtsham Ul Haq, Muhammad Usman Rashid, Muhammad Ishaq   +2 more
doaj   +1 more source

Depth and Stanley depth of the edge ideals of the powers of paths and cycles

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2019
Let k be a positive integer. We compute depth and Stanley depth of the quotient ring of the edge ideal associated to the kth power of a path on n vertices.
Iqbal Zahid, Ishaq Muhammad
doaj   +1 more source

Non-vanishing of Betti numbers of edge ideals and complete bipartite subgraphs [PDF]

, 2014
Given a finite simple graph one can associate the edge ideal. In this paper we prove that a graded Betti number of the edge ideal does not vanish if the original graph contains a set of complete bipartite subgraphs with some conditions.
Kimura, Kyouko
core  

Disordered but rhythmic—the role of intrinsic protein disorder in eukaryotic circadian timing

FEBS Letters, EarlyView.
Unstructured domains known as intrinsically disordered regions (IDRs) are present in nearly every part of the eukaryotic core circadian oscillator. IDRs enable many diverse inter‐ and intramolecular interactions that support clock function. IDR conformations are highly tunable by post‐translational modifications and environmental conditions, which ...
Emery T. Usher, Jacqueline F. Pelham
wiley   +1 more source