Adrian Dumitrescu

activity

20232025

most citedFailures of public key infrastructure: 53 year survey

1 citations · 1 across the 16 of their papers we have counts for

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math.CO2025

Note on the Number of Almost Ordinary Triangles

Adrian Dumitrescu, János Pach

Let $X$ be a set of $n$ points in the plane, not all on a line. According to the Gallai-Sylvester theorem, $X$ always spans an \emph{ordinary line}, i.e., one that passes through p…

math.CO2025

The number of regular simplices in higher dimensions

Felix Christian Clemen, Adrian Dumitrescu, Dingyuan Liu

We study the extremal function $S_{d}^{k} (n)$ , defined as the maximum number of regular $(k - 1)$ -simplices spanned by $n$ points in $R^{d}$ . For any fixed $d \geq 2 k \geq 6$ , we dete…

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.CO2025

On multiplicities of interpoint distances

Felix Christian Clemen, Adrian Dumitrescu, Dingyuan Liu

Given a set $X \subseteq R^{2}$ of $n$ points and a distance $d > 0$ , the multiplicity of $d$ is the number of times the distance $d$ appears between points in $X$ . Let $a_1(X)…

math.CO2024

Geometric Variants of the Gale--Berlekamp Switching Game

Adrian Dumitrescu

The Gale-Berlekamp switching game is played on the following device: $G_{n} = {1, 2, \dots, n} \times {1, 2, \dots, n}$ is an $n \times n$ array of lights is controlled by $2 n$ switche…

math.CO2024

Subset selection problems in planar point sets

József Balogh, Felix Christian Clemen, Adrian Dumitrescu +1

Given a finite point set satisfying condition $A$ , the subset selection problem asks, how large of a subset satisfying condition $B$ can be extracted? In this p…

math.CO2024

Maximizing the Maximum Degree in Ordered Nearest Neighbor Graphs

Péter Ágoston, Adrian Dumitrescu, Arsenii Sagdeev +2

For an ordered point set in a Euclidean space or, more generally, in an abstract metric space, the ordered Nearest Neighbor Graph is obtained by connecting each of the points to it…

math.CO2024

Partitioning Complete Geometric Graphs on Dense Point Sets into Plane Subgraphs

Adrian Dumitrescu, János Pach

A \emph{complete geometric graph} consists of a set $P$ of $n$ points in the plane, in general position, and all segments (edges) connecting them. It is a well known question of Bo…