volume 29, issue 1, P77-81 2002
DOI: 10.1007/s00454-002-2813-5
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Abstract: We exhibit a simple infinite family of series-parallel graphs that cannot be metrically embedded into Euclidean space with distortion smaller than ( log n). This matches Rao's [14] general upper bound for metric embedding of planar graphs into Euclidean space, thus resolving the question how well do planar metrics embed in Euclidean spaces?

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