Geodesic
On the Balance of Unrooted Trees
Journal of Graph Algorithms and Applications, Tome 25 (2021) no. 1, pp. 133-150.

Voir la notice de l'article provenant de la source Journal of Graph Algorythms and Applications website

We solve a class of optimization problems for (phylogenetic) $X$-trees or their shapes. These problems have recently appeared in different contexts, e.g. in the context of the impact of tree shapes on the size of TBR neighborhoods, but so far these problems have not been characterized and solved in a systematic way. In this work we generalize the concept and also present several applications. Moreover, our results give rise to a nice notion of balance for trees, which plays an important role in various different research areas, including mathematical phylogenetics as well as computer science. Unsurprisingly, so-called caterpillars are the most unbalanced tree shapes, but it turns out that balanced tree shapes cannot be described so easily as they need not even be unique. 
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Mareike Fischer; Volkmar Liebscher. On the Balance of Unrooted Trees. Journal of Graph Algorithms and Applications, Tome 25 (2021) no. 1, pp. 133-150. doi : 10.7155/jgaa.00553. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00553/

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