Geodesic
On the matching arrangement of a~graph and properties of its characteristic polynomial
Diskretnaya Matematika, Tome 35 (2023) no. 2, pp. 3-17

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We consider a hyperplane arrangement constructed from a subset of the set of all simple paths in a graph. A relation of the constructed arrangement to the maximum matching problem is established. In addition, the problem of finding the characteristic polynomial is reduced to the case of a connected original graph. In the case where the original graph is a tree, a formula for the characteristic polynomial is obtained.
Keywords: hyperplane arrangement, graphical arrangement, partially ordered set, matroid, maximal matching problem. 
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     title = {On the matching arrangement of a~graph and properties of its characteristic polynomial},
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A. I. Bolotnikov. On the matching arrangement of a~graph and properties of its characteristic polynomial. Diskretnaya Matematika, Tome 35 (2023) no. 2, pp. 3-17. http://geodesic.mathdoc.fr/item/DM_2023_35_2_a0/