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papers

Publications (36)

math.CO2019

Ordered graphs and large bi-cliques in intersection graphs of curves

Janos Pach, Istvan Tomon

An ordered graph $G_{<}$ is a graph with a total ordering $<$ on its vertex set. A monotone path of length $k$ is a sequence of vertices $v_{1} < v_{2} < \dots < v_{k}$ such that $v_{i} v_{j}$ is…

math.CO2018

A crossing lemma for multigraphs

Janos Pach, Geza Toth

Let $G$ be a drawing of a graph with $n$ vertices and $e > 4 n$ edges, in which no two adjacent edges cross and any pair of independent edges cross at most once. According to the cele…

math.CO2010

A computational approach to Conway's thrackle conjecture

Radoslav Fulek, Janos Pach

A drawing of a graph in the plane is called a thrackle if every pair of edges meets precisely once, either at a common vertex or at a proper crossing. Let t(n) denote the maximum n…

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…

math.FA2018

Controlling Lipschitz functions

Andrey Kupavskii, Janos Pach, Gabor Tardos

Given any positive integers $m$ and $d$ , we say the a sequence of points $(x_{i})_{i \in I}$ in $R^{m}$ is {\em Lipschitz- $d$ -controlling} if one can select suitable values $y_i…

math.CO2022

Quasiplanar Graphs, String Graphs, and the Erdos-Gallai Problem

Jacob Fox, Janos Pach, Andrew Suk

An $r$ -quasiplanar graph is a graph drawn in the plane with no $r$ pairwise crossing edges. Let $s \geq 3$ be an integer and $r = 2^{s}$ . We prove that there is a constant $C$ such tha…