Abstract
We exhibit a one-to-one correspondence between 3-colored graphs and subarrangements of certain hyperplane arrangements denoted <TEX>${\mathcal{J}}_n$</TEX>, <TEX>$n{\in}{\mathbb{N}}$</TEX>. We define the notion of centrality of 3-colored graphs, which corresponds to the centrality of hyperplane arrangements. Via the correspondence, the characteristic polynomial <TEX>${\chi}{\mathcal{J}}_n$</TEX> of <TEX>${\mathcal{J}}_n$</TEX> can be expressed in terms of the number of central 3-colored graphs, and we compute <TEX>${\chi}{\mathcal{J}}_n$</TEX> for n = 2, 3.
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