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We bound the hereditary discrepancy of a hypergraph $\mathcal{H}$ in two colors in terms of its hereditary discrepancy in $c$ colors. We show that $\mathrm{herdisc}(\mathcal{H},2)\leq Kc$ $\mathrm{herdisc}(\mathcal{H},c)$, where $K$ is some absolute constant. This bound is sharp apart from the absolute constant.

Hereditary Discrepancies in Different Numbers of Colors II