Publications by Gábor Tardos | EPFL Graph Search

On the Turan number of ordered forests

Gábor Tardos, Istvan Tomon, Dániel József Korándi

An ordered graph H is a simple graph with a linear order on its vertex set. The corresponding Turan problem, first studied by Pach and Tardos, asks for the maximum number ex(

ACADEMIC PRESS INC ELSEVIER SCIENCE2019

Planar Point Sets Determine Many Pairwise Crossing Segments

János Pach, Gábor Tardos

We show that any set of n points in general position in the plane determines n(1-o(1)) pairwise crossing segments. The best previously known lower bound, Omega(root n), was proved more than 25 years ago by Aronov, Erdos, Goddard, Kreitman, Krugerman, Pach, ...

ASSOC COMPUTING MACHINERY2019

Edge Ordered Turan Problems

Gábor Tardos, Abhishek Methuku

We introduce the Turan problem for edge ordered graphs. We call a simple graph edge ordered, if its edges are linearly ordered. An isomorphism between edge ordered graphs must respect the edge order. A subgraph of an edge ordered graph is itself an edge or ...

COMENIUS UNIV2019

Separation with restricted families of sets

János Pach, Gábor Tardos, Márton Naszódi, Zsolt Langi

Given a finite n-element set X, a family of subsets F subset of 2(X) is said to separate X if any two elements of X are separated by at least one member of F. It is shown that if vertical bar F vertical bar > 2(n-1), then one can select vertical bar log n ...

Academic Press Inc Elsevier Science2016

On the Richter-Thomassen Conjecture about Pairwise Intersecting Closed Curves

János Pach, Gábor Tardos

A long-standing conjecture of Richter and Thomassen states that the total number of intersection points between any n simple closed Jordan curves in the plane, so that any pair of them intersect and no three curves pass through the same point, is at least ...

Cambridge Univ Press2016

Cross-Intersecting Families of Vectors

János Pach, Gábor Tardos

Given a sequence of positive integers , let denote the family of all sequences of positive integers such that for all . Two families of sequences (or vectors), , are said to be -cross-intersecting if no matter how we select and , there are at least distinc ...

Springer Japan Kk2015

The visible perimeter of an arrangement of disks

János Pach, Gábor Tardos, Gabriel Nivasch

Given a collection of n opaque unit disks in the plane, we want to find a stacking order for them that maximizes their visible perimeter, the total length of all pieces of their boundaries visible from above. We prove that if the centers of the disks form ...

Elsevier Science Bv2014

The Visible Perimeter of an Arrangement of Disks

János Pach, Gábor Tardos, Gabriel Nivasch

Given a collection of n opaque unit disks in the plane, we want to find a stacking order for them that maximizes their visible perimeter, the total length of all pieces of their boundaries visible from above. We prove that if the centers of the disks form ...

Springer2013

The Range of a Random Walk on a Comb

János Pach, Gábor Tardos

The graph obtained from the integer grid Z x Z by the removal of all horizontal edges that do not belong to the x-axis is called a comb. In a random walk on a graph, whenever a walker is at a vertex v, in the next step it will visit one of the neighbors of ...

Electronic Journal Of Combinatorics2013

Piercing quasi-rectangles-On a problem of Danzer and Rogers

János Pach, Gábor Tardos

It is an old problem of Danzer and Rogers to decide whether it is possible to arrange 0(1/epsilon) points in the unit square so that every rectangle of area epsilon > 0 within the unit square contains at least one of them. We show that the answer to this q ...

Elsevier2012

Gábor Tardos

On the Turan number of ordered forests

Planar Point Sets Determine Many Pairwise Crossing Segments

Edge Ordered Turan Problems

Separation with restricted families of sets

On the Richter-Thomassen Conjecture about Pairwise Intersecting Closed Curves

Cross-Intersecting Families of Vectors

The visible perimeter of an arrangement of disks

The Visible Perimeter of an Arrangement of Disks

The Range of a Random Walk on a Comb

Piercing quasi-rectangles-On a problem of Danzer and Rogers

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On the Turan number of ordered forests

The visible perimeter of an arrangement of disks

Separation with restricted families of sets

Cross-Intersecting Families of Vectors

The Range of a Random Walk on a Comb

Piercing quasi-rectangles-On a problem of Danzer and Rogers

The Visible Perimeter of an Arrangement of Disks

Planar Point Sets Determine Many Pairwise Crossing Segments

Edge Ordered Turan Problems

On the Richter-Thomassen Conjecture about Pairwise Intersecting Closed Curves