In this article we introduce (combinatorial) multi-color discrepancy and generalize some classical results from 2-color discrepancy theory to c colors. We give a recursive method that constructs c-colorings from approximations to the 2-color discrepancy. This method works for a large class of theorems like the six-standard-deviation theorem of Spencer, the Beck-Fiala theorem and the results of Matoušsek, Welzl and Wernisch for bounded VC-dimension. On the other hand there are examples showing that discrepancy in c colors can not be bounded in terms of two-color discrepancy even if c is a power of 2. For the linear discrepancy version of the Beck-Fiala theorem the recursive approach also fails. Here we extend the method of floating colors to multi-colorings and prove multi-color versions of the the Beck-Fiala theorem and the Barany-Grunberg theorem.


Linear Discrepancy Weighted Discrepancy Color Discrepancy Discrepancy Theory Color Version 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Benjamin Doerr
    • 1
  • Anand Srivastav
    • 1
  1. 1.Mathematisches SeminarChristian-Albrechts-Universität zu KielKielGermany

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