Matching number, Hamiltonian graphs and discrete magnetic Laplacians

John Stewart Fabila Carrasco; Fernando Lledó; Olaf Post

doi:10.1016/j.laa.2022.02.006

Matching number, Hamiltonian graphs and discrete magnetic Laplacians

John Stewart Fabila Carrasco, Fernando Lledó, Olaf Post

School of Engineering

Research output: Contribution to journal › Article › peer-review

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.

Original language	Undefined/Unknown
Pages (from-to)	86-100
Journal	Linear algebra and its applications
Early online date	9 Feb 2022
DOIs	https://doi.org/10.1016/j.laa.2022.02.006
Publication status	Published - 1 Jun 2022

Access to Document

10.1016/j.laa.2022.02.006

https://arxiv.org/abs/2010.08828Licence: Other

Cite this

@article{342ba1d4bddc4784abc0ab17539674c9,

title = "Matching number, Hamiltonian graphs and discrete magnetic Laplacians",

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.",

author = "{Fabila Carrasco}, {John Stewart} and Fernando Lled{\'o} and Olaf Post",

year = "2022",

month = jun,

day = "1",

doi = "10.1016/j.laa.2022.02.006",

language = "Undefined/Unknown",

pages = "86--100",

journal = "Linear algebra and its applications",

issn = "0024-3795",

publisher = "Elsevier",

}

TY - JOUR

T1 - Matching number, Hamiltonian graphs and discrete magnetic Laplacians

AU - Fabila Carrasco, John Stewart

AU - Lledó, Fernando

AU - Post, Olaf

PY - 2022/6/1

Y1 - 2022/6/1

N2 - 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.

AB - 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.

U2 - 10.1016/j.laa.2022.02.006

DO - 10.1016/j.laa.2022.02.006

M3 - Article

SN - 0024-3795

SP - 86

EP - 100

JO - Linear algebra and its applications

JF - Linear algebra and its applications

ER -