• Publications
  • Influence
How to draw a planar graph on a grid
TLDR
Answering a question of Rosenstiehl and Tarjan, we show that every plane graph withn vertices has a Fáry embedding (i.e., straight-line embedding) on the 2n−4 byn−2 grid and provide an O(n) space,O(n logn) time algorithm to effect this embedding. Expand
  • 697
  • 51
Research problems in discrete geometry
TLDR
Note: Professor Pach's number: [045]; Also in: Facsimile edition: World Classics in Mathematics Series, vol. Expand
  • 709
  • 41
Embedding Planar Graphs at Fixed Vertex Locations
TLDR
We present an algorithm for constructing in O(n2) time a planar embedding of G mapping vertices to their assigned points and edges to polygonal curves with at least m/403 bends. Expand
  • 157
  • 25
  • PDF
On the Number of Incidences Between Points and Curves
  • J. Pach, M. Sharir
  • Mathematics, Computer Science
  • Comb. Probab. Comput.
  • 1 March 1998
TLDR
We apply an idea of Szekely to prove a general upper bound on the number of incidences between a set m points and a set of n well-behaved curves in the plane. Expand
  • 146
  • 23
Repeated Angles in the Plane and Related Problems
TLDR
We show that a set of points in the plane determine O(n2 log n) triples that define the same angle α, and that for many angles α (including π 2 ) this bound is tight in the worst case. Expand
  • 90
  • 20
  • PDF
Forbidden paths and cycles in ordered graphs and matrices
At most how many edges can an ordered graph ofn vertices have if it does not contain a fixed forbidden ordered subgraphH? It is not hard to give an asymptotically tight answer to this question,Expand
  • 61
  • 20
Graphs Drawn with Few Crossings Per Edge
  • J. Pach, G. Tóth
  • Mathematics, Computer Science
  • Graph Drawing
  • 18 September 1996
TLDR
We show that if a graph of v vertices can be drawn in the plane so that every edge crosses at most k> 0 others, then its number of edges cannot exceed 4. Expand
  • 105
  • 17
  • PDF
Conflict-Free Colourings of Graphs and Hypergraphs
  • J. Pach, G. Tardos
  • Computer Science, Mathematics
  • Combinatorics, Probability and Computing
  • 1 September 2009
TLDR
A colouring of the vertices of a hypergraph H is called conflict-free if each hyperedge E of H contains a vertex of ‘unique’ colour that does not get repeated in E. Expand
  • 74
  • 17
  • PDF
Ramsey-type Theorems with Forbidden Subgraphs
TLDR
Dedicated to the memory of Paul ErdősA graph is called H-free if it contains no induced copy of H. Expand
  • 93
  • 17
  • PDF
...
1
2
3
4
5
...