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The Beginnings of Geometric Graph Theory

  • János Pach
Part of the Bolyai Society Mathematical Studies book series (BSMS, volume 25)

Abstract

Geometric graphs (topological graphs) are graphs drawn in the plane with possibly crossing straight-line edges (resp., curvilinear edges). Starting with a problem of Heinz Hopf and Erika Pannwitz from 1934 and a seminal paper of Paul Erdős from 1946, we give a biased survey of Turán-type questions in the theory of geometric and topological graphs. What is the maximum number of edges that a geometric or topological graph of n vertices can have if it contains no forbidden subconfiguration of a certain type? We put special emphasis on open problems raised by Erdős or directly motivated by his work.

Keywords

Chromatic Number Topological Graph Geometric Graph Combinatorial Geometry Disjoint Edge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© János Bolyai Mathematical Society and Springer-Verlag 2013

Authors and Affiliations

  • János Pach
    • 1
    • 2
  1. 1.EPFLLausanneSwitzerland
  2. 2.Alfréd Rényi Institute of MathematicsHungarian Academy of SciencesBudapestHungary

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