On the matching arrangement of a graph and properties of its characteristic polynomial
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Alexey I. Bolotnikov
Abstract
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.
Originally published in Diskretnaya Matematika (2023) 35, №2, 3–17 (in Russian).
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Articles in the same Issue
- Frontmatter
- On the matching arrangement of a graph and properties of its characteristic polynomial
- Realization of even permutations of even degree by products of four involutions without fixed points
- On implicit extensions in many-valued logic
- On radio graceful Hamming graphs of any diameter
- Limit joint distribution of the statistics of «Monobit test», «Frequency Test within a Block» and «Test for the Longest Run of Ones in a Block»
- Resistance distance and Kirchhoff index of two kinds of double join operations on graphs
Articles in the same Issue
- Frontmatter
- On the matching arrangement of a graph and properties of its characteristic polynomial
- Realization of even permutations of even degree by products of four involutions without fixed points
- On implicit extensions in many-valued logic
- On radio graceful Hamming graphs of any diameter
- Limit joint distribution of the statistics of «Monobit test», «Frequency Test within a Block» and «Test for the Longest Run of Ones in a Block»
- Resistance distance and Kirchhoff index of two kinds of double join operations on graphs
