Matching number, Hamiltonian graphs and discrete magnetic Laplacians
In this article, we relate the spectrum of the discrete magnetic Laplacian (DML) on a finite simple graph with two structural properties of the graph: the existence of a perfect matching and the existence of a Hamiltonian cycle of the underlying graph. In particular, we give a family of spectral obs...
| Main Authors: | , , |
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| Format: | Article in Journal/Newspaper |
| Language: | unknown |
| Published: |
arXiv
2020
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| Subjects: | |
| Online Access: | https://dx.doi.org/10.48550/arxiv.2010.08828 https://arxiv.org/abs/2010.08828 |
| Summary: | In this article, we relate the spectrum of the discrete magnetic Laplacian (DML) on a finite simple graph with two structural properties of the graph: the existence of a perfect matching and the existence of a Hamiltonian cycle of the underlying graph. In particular, we give a family of spectral obstructions parametrised by the magnetic potential for the graph to be matchable (i.e., having a perfect matching) or for the existence of a Hamiltonian cycle. We base our analysis on a special case of the spectral preorder introduced in [FCLP20a] and we use the magnetic potential as a spectral control parameter. : 9 pages, 4 figures |
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