Bulletin of the
Korean Mathematical Society BKMS

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

Keywords: hyperplane arrangements, bipartite graphs, colored graphs

MSC numbers: 32S22, 05C30