Construction of a hyperplane arrangement with a specific set of simple paths in a graph and its properties

There exists a way to calculate the amount of regions of a hyperplane arrangement using its characteristic polynomial. This allows using hyperplane arrangements in solutions of combinatorial problems. This paper considers a hyperplane arrangement constructed with a subset of a set of all simple paths in a graph. Results in this paper connect this arrangement to the maximum matching problem and allow to calculate its characteristic polynomial for specific cases of the initial graph.