Publication date
May 2002
DOI Publisher
Elsevier Science B.V. ISSN
0012-365XAbstract
AbstractIn this article, we investigate the interrelation between the discrepancies of a given hypergraph in different numbers of colors. Being an extreme example we determine the multi-color discrepancies of the k-balanced hypergraph Hnk on partition classes of (equal) size n. Let c,k,n∈N. Set k0≔kmodc and bnkc≔(n−⌊n/⌈c/k⌉⌋)k/c. For the discrepancy in c colors we showbnk0c⩽disc(Hnk,c)<bnk0c+1,if k0≠0, and disc(Hnk,c)=0, if c divides k. This shows that, in general, there is little correlation between the discrepancies of Hnk in different numbers of colors. If c divides k though, disc(H,c)⩽(k/c)disc(H,k) holds for any hypergraph H
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