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Asymptotic connectivity, hamiltonicity and toughness
Abstract
We define coarse variants of the notions of connectivity, hamiltonicity, toughness, and spanning trees. Our notions are invariant under quasi-isometries, and they obey the same relationships between them as their classical analogs. We pose several open problems that are coarse versions of classical results and conjectures about hamiltonicity.
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BibTeX
@misc{georgakopoulos2026asymptotic,
title = {{Asymptotic connectivity, hamiltonicity and toughness}},
author = {Agelos Georgakopoulos},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.09992},
eprint = {2610.09992},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.09992},
}
RIS
TY - UNPB
TI - Asymptotic connectivity, hamiltonicity and toughness
AU - Agelos Georgakopoulos
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.09992
UR - https://arxiv.org/abs/2610.09992
AB - We define coarse variants of the notions of connectivity, hamiltonicity, toughness, and spanning trees. Our notions are invariant under quasi-isometries, and they obey the same relationships between them as their classical analogs. We pose several open problems that are coarse versions of classical results and conjectures about hamiltonicity.
ER -