Geodesic
The functions that do not change types of minimal fillings
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2015), pp. 42-45

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It is proved that a function measuring distances in metric spaces and preserving the types of their minimal fillings has the form $f(x)=kx+b$. It is sufficient to assume in this case that the types of fillings are preserved for spaces consisting of not more than five points. 
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     author = {S. Yu. Lipatov},
     title = {The functions that do not change types of minimal fillings},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
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     year = {2015},
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     url = {http://geodesic.mathdoc.fr/item/VMUMM_2015_6_a6/}
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S. Yu. Lipatov. The functions that do not change types of minimal fillings. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2015), pp. 42-45. http://geodesic.mathdoc.fr/item/VMUMM_2015_6_a6/