Asymptotic connectivity, hamiltonicity and toughness

Agelos Georgakopoulos

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arXiv · 2610.09992

Asymptotic connectivity, hamiltonicity and toughness

Agelos Georgakopoulos

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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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Agelos Georgakopoulos. 2026-10-07. Asymptotic connectivity, hamiltonicity and toughness. https://arxiv.org/abs/2610.09992

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