Geodesic
The twist number of planar linear trees
Sbornik. Mathematics, Tome 187 (1996) no. 8, pp. 1149-1195

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New natural geometric characteristics are introduced for planar linear trees: the boundary set and the twist number. It turns out that the number of convexity levels of the boundary set is bounded above by a linear function of the twist number. As consequences of this general fact, some non-trivial assertions are obtained about the geometry of linear trees that are extremals of the length or weight functional. 
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     author = {A. O. Ivanov and A. A. Tuzhilin},
     title = {The twist number of planar linear trees},
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     number = {8},
     year = {1996},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1996_187_8_a1/}
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A. O. Ivanov; A. A. Tuzhilin. The twist number of planar linear trees. Sbornik. Mathematics, Tome 187 (1996) no. 8, pp. 1149-1195. http://geodesic.mathdoc.fr/item/SM_1996_187_8_a1/