Extremal Problems for Discrepancy

  • L. Lovász
  • K. Vesztergombi
Part of the Algorithms and Combinatorics 8 book series (AC, volume 8)


We determine the maximum number of edges in a hypergraph with a given number of vertices and given hereditary discrepancy. We derive bounds on the maximum number of rows in an integral matrix with a given number of columns and with given hereditary discrepancy. The main tool is a geometric interpretation of discrepancy and a relation between the volumes of polar convex bodies.


Convex Body Extremal Problem Linear Discrepancy Unit Cube Integral Vector 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • L. Lovász
    • 1
  • K. Vesztergombi
    • 2
  1. 1.Department of Computer ScienceL. Eötvös UniversityBudapestHungary
  2. 2.Faculty of Electrical Engineering, Department of MathematicsBudapest University of TechnologyBudapestHungary

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