The twist number of planar linear trees
Alexander Ivanov, Alexey Avgustinovich Tuzhilin · Sbornik Mathematics · 1996
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.