Matching number, Hamiltonian graphs and magnetic Laplacian matrices

John Stewart Fabila-Carrasco, Fernando Lledó*, Olaf Post

*Corresponding author for this work

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 [8], and we use the magnetic potential as a spectral control parameter.

Original languageEnglish
Pages (from-to)86-100
Number of pages15
JournalLinear algebra and its applications
Volume642
Early online date9 Feb 2022
DOIs
Publication statusPublished - 1 Jun 2022

Keywords / Materials (for Non-textual outputs)

  • Discrete magnetic Laplacian
  • Hamiltonian graph
  • Matching number
  • Spectral graph theory

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