Browsing by Author "Saeedi Madani, Sara"

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    Diameter and Connectivity of Finite Simple Graphs II
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2024) Hibi, Takayuki; Saeedi Madani, Sara
    Let $G$ be a finite simple non-complete connected graph on $[n] = \{1, \ldots, n\}$ and $\kappa(G) \geq 1$ its vertex connectivity. Let $f(G)$ denote the number of free vertices of $G$ and $\mathrm{diam}(G)$ the diameter of $G$. The final goal of this paper is to determine all sequences of integers $(n,f,d,k)$ with $n\geq 8$, $f\geq 0$, $d\geq 2$ and $k\geq 1$ for which there exists a finite simple non-complete connected graph on $[n]$ with $f=f(G)$, $d=\mathrm{diam}(G)$ and $k=\kappa(G)$.
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    Matchings and Squarefree Powers of Edge Ideals
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2019) Erey, Nursel; Herzog, Jürgen; Hibi, Takayuki; Saeedi Madani, Sara
    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, and we consider the question of when such powers are linearly related or have linear resolution. We also consider the so-called squarefree Ratliff property.