2 problems

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Non-singleton optimal clusters for the graph-distance objective
Non-singleton optimal-cluster conjecture. If $d_G$ is not an ultrametric, then for some optimal value of $\epsilon$ , neither $H_\epsilon$ nor all $C\in\mathcal(\Gamma_\epsilon)$ ar…
Conjectureopengraph-theory optimization ultrametric-metric-spacesarXiv posted 2 days ago
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Vietoris–Rips ultrametric condition for Laplacian approximation
Vietoris–Rips ultrametric condition. The Vietoris–Rips clusters for some $\epsilon>0$ realise the sufficient ultrametric condition
Conjectureopengraph-laplacians ultrametric-metric-spaces vietoris-rips-complexesarXiv posted 2 days ago

Non-singleton optimal clusters for the graph-distance objective