Pavel Valtr

collaborators

2 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…