Erdős-Hajnal-type Results on Intersection Patterns of Geometric Objects

  • Jacob Fox
  • János Pach
Part of the Bolyai Society Mathematical Studies book series (BSMS, volume 17)


In their seminal paper [21], Erdős and Hajnal raised the following question. Is it true that for any graph G there exists a constant c = c(G) > 0 with the property that every graph of n vertices that contains no induced subgraph isomorphic to G has a complete or an empty induced subgraph of size n c ? We answer this question in the affirmative for some special classes of graphs denned by geometric methods.


Convex Body Chromatic Number Geometric Object Intersection Graph Intersection Pattern 
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 2008

Authors and Affiliations

  • Jacob Fox
    • 1
  • János Pach
    • 2
  1. 1.Department of MathematicsPrinceton UniversityPrincetonUSA
  2. 2.City College, CUNY and Courant InstituteNYUNew YorkUSA

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