On certain hyperplane arrangements and colored graphs
Bull. Korean Math. Soc. 2017 Vol. 54, No. 2, 375-382
Published online March 20, 2017
Printed March 31, 2017
Joungmin Song
Abstract : 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
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