Matching number, Hamiltonian graphs and discrete magnetic Laplacians

John Stewart Fabila Carrasco, Fernando Lledó, Olaf Post

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

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.
Original languageUndefined/Unknown
Pages (from-to)86-100
JournalLinear algebra and its applications
Early online date9 Feb 2022
Publication statusPublished - 1 Jun 2022

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