M. Saghafian

activity

20172026

most citedOn

k

-tuple and

k

-tuple total domination numbers of regular graphs

1 citations · 1 across the 9 of their papers we have counts for

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6 papers · 1 filter

math.CO2025

Covering Complete Geometric Graphs by Monotone Paths

Adrian Dumitrescu, János Pach, Morteza Saghafian +1

Given a set $A$ of $n$ points (vertices) in general position in the plane, the \emph{complete geometric graph} $K_{n} [A]$ consists of all $(2 n)$ segments (edges) between the…

math.CO2024

On Spheres with $k$ Points Inside

Herbert Edelsbrunner, Alexey Garber, Morteza Saghafian

We generalize the classic definition of Delaunay triangulation and prove that for a locally finite and coarsely dense generic point set, $A \subseteq R^{d}$ , the $d$ -simplic…

math.CO2023

Order-2 Delaunay Triangulations Optimize Angles

Herbert Edelsbrunner, Alexey Garber, Morteza Saghafian

The local angle property of the (order- $1$ ) Delaunay triangulations of a generic set in $R^{2}$ asserts that the sum of two angles opposite a common edge is less than $π$ . T…

math.CO2023

Decomposition of Geometric Graphs into Star Forests

János Pach, Morteza Saghafian, Patrick Schnider

We solve a problem of Dujmović and Wood (2007) by showing that a complete convex geometric graph on $n$ vertices cannot be decomposed into fewer than $n - 1$ star-forests, each consi…

math.CO2017

Chromatic Number and Dichromatic Polynomial of Digraphs

Saeed Akbari, Amir Hossein Ghodrati, Afrouz Jabalameli +1

Let $G$ be a graph of order $n$ . It is well-known that $α (G) \geq \sum_{i = 1}^{n} \frac{1}{1 + d _{i}}$ , where $α (G)$ is the independence number of $G$ and $d_{1}, \dots, d_{n}$ is the degree se…

math.CO2017★ 1 cited

On $k$ -tuple and $k$ -tuple total domination numbers of regular graphs

Sharareh Alipour, Amir Jafari, Morteza Saghafian

Let $G$ be a connected graph of order $n$ , whose minimum vertex degree is at least $k$ . A subset $S$ of vertices in $G$ is a $k$ -tuple total dominating set if every vertex of $G$ i…