Matching number, Hamiltonian graphs and discrete magnetic Laplacians

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 obs...

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Bibliographic Details
Main Authors: Fabila-Carrasco, J. S., Lledó, Fernando, Post, Olaf
Format: Article in Journal/Newspaper
Language:unknown
Published: arXiv 2020
Subjects:
Combinatorics math.CO
Mathematical Physics math-ph
Spectral Theory math.SP
FOS Mathematics
FOS Physical sciences
05C70, 05C45, 39A70, 47A10, 05C50
DML
Online Access:https://dx.doi.org/10.48550/arxiv.2010.08828
https://arxiv.org/abs/2010.08828
id ftdatacite:10.48550/arxiv.2010.08828
record_format openpolar
spelling ftdatacite:10.48550/arxiv.2010.08828 2023-05-15T16:01:48+02:00 Matching number, Hamiltonian graphs and discrete magnetic Laplacians Fabila-Carrasco, J. S. Lledó, Fernando Post, Olaf 2020 https://dx.doi.org/10.48550/arxiv.2010.08828 https://arxiv.org/abs/2010.08828 unknown arXiv arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ Combinatorics math.CO Mathematical Physics math-ph Spectral Theory math.SP FOS Mathematics FOS Physical sciences 05C70, 05C45, 39A70, 47A10, 05C50 Article CreativeWork article Preprint 2020 ftdatacite https://doi.org/10.48550/arxiv.2010.08828 2022-03-10T15:09:53Z 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. : 9 pages, 4 figures Article in Journal/Newspaper DML DataCite Metadata Store (German National Library of Science and Technology)
institution Open Polar
collection DataCite Metadata Store (German National Library of Science and Technology)
op_collection_id ftdatacite
language unknown
topic Combinatorics math.CO
Mathematical Physics math-ph
Spectral Theory math.SP
FOS Mathematics
FOS Physical sciences
05C70, 05C45, 39A70, 47A10, 05C50
spellingShingle Combinatorics math.CO
Mathematical Physics math-ph
Spectral Theory math.SP
FOS Mathematics
FOS Physical sciences
05C70, 05C45, 39A70, 47A10, 05C50
Fabila-Carrasco, J. S.
Lledó, Fernando
Post, Olaf
Matching number, Hamiltonian graphs and discrete magnetic Laplacians
topic_facet Combinatorics math.CO
Mathematical Physics math-ph
Spectral Theory math.SP
FOS Mathematics
FOS Physical sciences
05C70, 05C45, 39A70, 47A10, 05C50
description 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. : 9 pages, 4 figures
format Article in Journal/Newspaper
author Fabila-Carrasco, J. S.
Lledó, Fernando
Post, Olaf
author_facet Fabila-Carrasco, J. S.
Lledó, Fernando
Post, Olaf
author_sort Fabila-Carrasco, J. S.
title Matching number, Hamiltonian graphs and discrete magnetic Laplacians
title_short Matching number, Hamiltonian graphs and discrete magnetic Laplacians
title_full Matching number, Hamiltonian graphs and discrete magnetic Laplacians
title_fullStr Matching number, Hamiltonian graphs and discrete magnetic Laplacians
title_full_unstemmed Matching number, Hamiltonian graphs and discrete magnetic Laplacians
title_sort matching number, hamiltonian graphs and discrete magnetic laplacians
publisher arXiv
publishDate 2020
url https://dx.doi.org/10.48550/arxiv.2010.08828
https://arxiv.org/abs/2010.08828
genre DML
genre_facet DML
op_rights arXiv.org perpetual, non-exclusive license
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
op_doi https://doi.org/10.48550/arxiv.2010.08828
_version_ 1766397523572817920

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