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arXiv · 2010.08828

Matching number, Hamiltonian graphs and discrete magnetic Laplacians

J. S. Fabila-Carrasco·Fernando Lledó·Olaf Post
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Abstract

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.

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J. S. Fabila-Carrasco, Fernando Lledó, Olaf Post. 2020-10-17. Matching number, Hamiltonian graphs and discrete magnetic Laplacians. https://doi.org/10.1016/j.laa.2022.02.006

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