M. Saghafian

activity

20242026

collaborators

9 papers

cs.CG2026

How Close is a Tree to a Euclidean Minimum Spanning Tree?

Todor AntiÄ, JiÅÃ Fiala, Jelena GliÅ¡iÄ +8

Let $I^$ be a straight-line crossing-free drawing of a tree $T$ . A \emph{bad pair} in $I^$ is a pair of non-adjacent vertices of $T$ whose Euclidean distance in $I^$ is smaller tha…

cs.CG2026

How many times can two minimum spanning trees cross?

Todor Antić, Todor AntiÄ, Morteza Saghafian +5

Let $P$ be a generic set of $n$ points in the plane, and let $P = R \cup B$ be a coloring of $P$ in two colors. We are interested in the number of crossings between the minimum spanni…

math.CO2026

Covering Complete Geometric Graphs by Monotone Paths

Adrian Dumitrescu, JÃ¡nos 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…

cs.CG2025

Edge-Constrained Hamiltonian Paths on a Point Set

Todor AntiÄ, Aleksa DÅ¾uklevski, JiÅÃ Fiala +5

Let S be a set of distinct points in general position in the Euclidean plane. A plane Hamiltonian path on S is a crossing-free geometric path such that every point of S is a vertex…

math.PR2025

Expected Length of the Euclidean Minimum Spanning Tree and 1-norms of Chromatic Persistence Diagrams in the Plane

OndÅej Draganov, Herbert Edelsbrunner, Sophie Rosenmeier +1

Let $c$ be the constant such that the expected length of the Euclidean minimum spanning tree of $n$ random points in the unit square is $c n$ in the limit, when $n$ goes to…

math.CO2025

Flips in Two-dimensional Hypertriangulations

Herbert Edelsbrunner, Alexey Garber, Mohadese Ghafari +2

We study flips in hypertriangulations of planar points sets. Here a level- $k$ hypertriangulation of $n$ points in the planes is a subdivision induced by the projection of a $k$ -hyp…