Todor Antic

collaborators

5 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…

math.CO2026

Two Results on Outer-String Graphs

Todor AntiÄ, VÃt JelÃnek, Jan KratochvÃl +1

An \emph{outer-string representation} of a graph $G$ is an intersection representation of $G$ where vertices are represented by curves (strings) inside the unit disk and each curve…

cs.CG2026

Hypercube drawings with no long plane paths

Todor AntiÄ, Niloufar Fuladi, Anna Margarethe Limbach +1

We study the existence of plane substructures in drawings of the $d$ -dimensional hypercube graph $Q_{d}$ . We construct drawings of $Q_{d}$ which contain no plane subgraph with more tha…

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.CO2025

Crossing and non-crossing families

Todor AntiÄ, Martin Balko, Birgit Vogtenhuber

For a finite set $P$ of points in the plane in general position, a \emph{crossing family} of size $k$ in $P$ is a collection of $k$ line segments with endpoints in $P$ that are pai…