Geodesic
Non-existence of distinct codirected locally minimal trees on a plane
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2009), pp. 21-25

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Locally minimal graphs on a plane are considered. A simpler proof is given for the uniqueness of a globally minimal spanning tree on a plane in the general case. The proof presented here uses only local minimality of trees and is of independent interest. 
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     author = {K. I. Oblakov},
     title = {Non-existence of distinct codirected locally minimal trees on a plane},
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     publisher = {mathdoc},
     number = {2},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2009_2_a4/}
}
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K. I. Oblakov. Non-existence of distinct codirected locally minimal trees on a plane. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2009), pp. 21-25. http://geodesic.mathdoc.fr/item/VMUMM_2009_2_a4/