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In this article, we will prove that the set of 4-dissimilarity vectors ofn-trees is contained in the tropical Grassmannian G_{4,n}. We will also proposethree equivalent conjectures related to the set of m-dissimilarity vectors ofn-trees for the case m > 4. Using a computer algebra system, we can prove theseconjectures for m = 5.

On the relation between weighted trees and tropical Grassmannians