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This paper contains a description of a connection between the matchingarrangement and the matching polyhedron. A bijection between regions of thematching arragement and LP-orientations of the matching polyhedron isconstructed. This bijection allows to calculate the number of LP-orientationsof the matching polyhedron with the characteristic polynomial of the matchingarrangement.

On a matching arrangement of a graph and LP-orientations of a matching polyhedron