J. Pach

collaborators

4 papers

math.CO2026

On traces of randomly rolling polytopes

Kenneth Moore, János Pach

Let $P$ be a three-dimensional convex polytope resting with one of its faces on the plane. At each step, $P$ is allowed to roll over a randomly selected edge of…

math.CO2026

How large part of a graph can be covered by the neighborhoods of k vertices?

Janos Pach

Let $k \geq 2$ be fixed integer, $0 < c < 1$ a constant. Consider a graph $G$ with $n$ vertices and average degree $c n$ . We answer a question of Simon Griffiths by showing that $G$ has $…

math.CO2025

Nearly equal distances in the plane, II

P. ErdÅs, E. Makai, J. Pach

Let ${p_{1}, \dots, p_{n}} \subset R^{2}$ be a separated point set, i.e., any two points have a distance at least $1$ . Let $k \geq 1$ be an integer, and $1 \le t_1 < \ldots <…

math.CO2025

Is the space of reachable particle configurations dense?

Janos Pach, Gabor Tardos

Let $p_{0}, \dots, p_{n}$ be a finite sequence of points in an Euclidean space $R^{d}$ . Suppose that there is a (pointlike) particle sitting at each point $p_{i}$ . In a ``legal'' move, any…