Matching number, Hamiltonian graphs and discrete magnetic Laplacians
Combinatorics
2022-07-11 v1 Mathematical Physics
math.MP
Spectral Theory
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
Cite
@article{arxiv.2010.08828,
title = {Matching number, Hamiltonian graphs and discrete magnetic Laplacians},
author = {J. S. Fabila-Carrasco and Fernando Lledó and Olaf Post},
journal= {arXiv preprint arXiv:2010.08828},
year = {2022}
}
Comments
9 pages, 4 figures