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An Open Family of Sets That Have Several Minimal Fillings


Minimal fillings of n-point metric spaces were introduced by Ivanov and Tuzhilin. It was thought that “for almost all sets” in some sense such a filling is unique. Here we introduce a counterexample to this hypothesis.

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    A. Yu. Eremin, “A formula for the weight of a minimal filling of a finite metric space,” Mat. Sb., 204, No. 9, 51–72 (2013).

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Correspondence to Z. Ovsyannikov.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 18, No. 2, pp. 153–156, 2013.

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Ovsyannikov, Z. An Open Family of Sets That Have Several Minimal Fillings. J Math Sci 203, 855–857 (2014).

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