S. Madani

activity

20132026

most citedThe regularity of binomial edge ideals of graphs

10 citations · 24 across the 13 of their papers we have counts for

collaborators

20 papers

math.AC2026

Depth and Krull dimension of Binomial edge ideals

Takayuki Hibi, Sara Saeedi Madani

Let $J_{G}$ denote the binomial edge ideal of a finite graph $G$ in the polynomial ring $S$ . We determine all triples $(n, t, d)$ with $n \geq 3$ for which there exists a finite connect…

math.AC2026

Prime and Cohen--Macaulay binomial ideals with linear resolution

Takayuki Hibi, Ayesha Asloob Qureshi, Sara Saeedi Madani

Let $I$ be an ideal of a polynomial ring $S$ over a field $K$ for which $I$ is minimally generated by at least two quadratic binomials. Suppose that (i) $I$ is prime, (ii) $S / I$ is…

math.AC2025

Minimal primes and radicality of ideals generated by adjacent 2-minors

Takayuki Hibi, Francesco Navarra, Ayesha Asloob Qureshi +1

In this paper, we provide a complete description of the minimal primes of ideals generated by adjacent $2$ -minors, in terms of the so-called admissible sets and associated lattice…

math.AC2025

Binomial edge ideals of Cameron-Walker graphs

Takayuki Hibi, Sara Saeedi Madani

Let $G$ be a Cameron--Walker graph on $n$ vertices and $J_{G}$ the binomial edge ideal of $G$ . Let $S$ denote the polynomial ring in $2 n$ variables over a field. It is shown that the…

math.AC2025

Complementary edge ideals

Takayuki Hibi, Ayesha Asloob Qureshi, Sara Saeedi Madani

In this paper, we introduce the concept of complementary edge ideals of graphs and study their algebraic properties and invariants.

math.CO2024

Diameter and connectivity of finite simple graphs II

Takayuki Hibi, Sara Saeedi Madani

Let $G$ be a finite simple non-complete connected graph on $[n] = {1, \dots, n}$ and $κ (G) \geq 1$ its vertex connectivity. Let $f (G)$ denote the number of free vertices of $G$ …

math.AC2022

Hankel edge ideals of trees and (semi-)Hamiltonian graphs

Dariush Kiani, Sara Saeedi Madani, Saeed Tafazolian

In this paper, we study the Hankel edge ideals of graphs. We determine the minimal prime ideals of the Hankel edge ideal of labeled Hamiltonian and semi-Hamiltonian graphs, and we…

math.AC2021

On the depth of binomial edge ideals of graphs

Mohammad Rouzbahani Malayeri, Sara Saeedi Madani, Dariush Kiani

Let $G$ be a graph on the vertex set $[n]$ and $J_{G}$ the associated binomial edge ideal in the polynomial ring $S = K [x_{1}, \dots, x_{n}, y_{1}, \dots, y_{n}]$ . In this paper we inves…

math.AC2020

Binomial edge ideals of small depth

Mohammad Rouzbahani Malayeri, Sara Saeedi Madani, Dariush Kiani

Let $G$ be a graph on $[n]$ and $J_{G}$ be the binomial edge ideal of $G$ in the polynomial ring $S = K [x_{1}, \dots, x_{n}, y_{1}, \dots, y_{n}]$ . In this paper we investigate some topo…

math.AC2020★ 2 cited

A proof for a conjecture on the regularity of binomial edge ideals

M. Rouzbahani Malayeri, S. Saeedi Madani, D. Kiani

In this paper we introduce the concept of clique disjoint edge sets in graphs. Then, for a graph $G$ , we define the invariant $η (G)$ as the maximum size of a clique disjoint edge s…

math.AC2019

Matchings and squarefree powers of edge ideals

Nursel Erey, Jürgen Herzog, Takayuki Hibi +1

Squarefree powers of edge ideals are intimately related to matchings of the underlying graph. In this paper we give bounds for the regularity of squarefree powers of edge ideals, a…

math.AC2017

Binomial edge ideals of regularity $3$

Sara Saeedi Madani, Dariush Kiani

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 ch…

math.AC2016★ 8 cited

Retracts and algebraic properties of cut algebras

Tim Roemer, Sara Saeedi Madani

We study cut algebras which are toric rings associated to graphs. The key idea is to consider suitable retracts to understand algebraic properties and invariants of such algebras l…

math.AC2015

The linear strand of determinantal facet ideals

Jürgen Herzog, Dariush Kiani, Sara Saeedi Madani

Let $X$ be an $(m \times n)$ -matrix of indeterminates, and let $J$ be the ideal generated by a set $S$ of maximal minors of $X$ . We construct the linear strand of the reso…

math.CO2015

Cohen-Macaulay and Gorenstein path ideals of trees

Sara Saeedi Madani, Dariush Kiani

Let $R = k [x_{1}, \dots, x_{n}]$ , where $k$ is a field. The path ideal (of length $t \geq 2$ ) of a directed graph $G$ is the monomial ideal, denoted by $I_{t} (G)$ , whose generators cor…

math.AC2015★ 1 cited

The Castelnuovo-Mumford regularity of binomial edge ideals

Dariush Kiani, Sara Saeedi Madani

We prove a conjectured upper bound for the Castelnuovo-Mumford regularity of binomial edge ideals of graphs, due to Matsuda and Murai. Indeed, we prove that $\mathrm{reg}(J_G)\leq…

math.AC2014★ 3 cited

On the ideal of orthogonal representations of a graph in $R^{2}$

Jürgen Herzog, Antonio Macchia, Sara Saeedi Madani +1

In this paper, we study orthogonal representations of simple graphs $G$ in $R^{d}$ from an algebraic perspective in case $d = 2$ . Orthogonal representations of graphs, intro…

math.AC2014

The coordinate ring of a simple polyomino

Juergen Herzog, Sara Saeedi Madani

In this paper it is shown that a polyomino is balanced if and only if it is simple. As a consequence one obtains that the coordinate ring of a simple polyomino is a normal Cohen-Ma…

math.AC2014

Pseudo-Gorenstein and level Hibi rings

Viviana Ene, Jürgen Herzog, Takayuki Hibi +1

We introduce pseudo-Gorenstein rings and characterize those Hibi rings attached to a finite distributive lattice L which are pseudo-Gorenstein. The characterization is given in ter…

math.AC2013★ 10 cited

The regularity of binomial edge ideals of graphs

Dariush Kiani, Sara Saeedi Madani

We prove two recent conjectures on some upper bounds for the Castelnuovo-Mumford regularity of the binomial edge ideals of some different classes of graphs. We prove the conjecture…

Depth and Krull dimension of Binomial edge ideals

Prime and Cohen--Macaulay binomial ideals with linear resolution

Minimal primes and radicality of ideals generated by adjacent 2-minors

Binomial edge ideals of Cameron-Walker graphs

Complementary edge ideals

Diameter and connectivity of finite simple graphs II

Hankel edge ideals of trees and (semi-)Hamiltonian graphs

On the depth of binomial edge ideals of graphs

Binomial edge ideals of small depth

A proof for a conjecture on the regularity of binomial edge ideals

Matchings and squarefree powers of edge ideals

Binomial edge ideals of regularity 3

Retracts and algebraic properties of cut algebras

The linear strand of determinantal facet ideals

Cohen-Macaulay and Gorenstein path ideals of trees

The Castelnuovo-Mumford regularity of binomial edge ideals

On the ideal of orthogonal representations of a graph in R2

The coordinate ring of a simple polyomino

Pseudo-Gorenstein and level Hibi rings

The regularity of binomial edge ideals of graphs

Binomial edge ideals of regularity $3$

On the ideal of orthogonal representations of a graph in $R^{2}$