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On the matching arrangement of a graph and properties of its characteristic polynomial

This paper considers a hyperplane arrangement constructed with a subset of a set of all simple paths in a graph. A connection of the constructed arrangement to the maximum matching problem is established. Moreover, the problem of finding the characteristic polynomial is reduced to the case of a connected initial graph. The formula of the characteristic polynomial was also found for the case, when the initial graph is a tree.

preprint2022arXivOpen access
Aleksey Bolotnikov
math.CO
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Aleksey Bolotnikov

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