Matching number, Hamiltonian graphs and discrete magnetic Laplacians Articles uri icon

publication date

  • October 2020

start page

  • 1

end page

  • 9

International Standard Serial Number (ISSN)

  • WWWW-0074

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.

keywords

  • spectral graph theory; discrete magnetic laplacian; matching number; hamiltonian graph