Convex Realizations of Planar Linear Trees
Matematičeskie zametki, Tome 73 (2003) no. 5, pp. 665-675.

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We prove a necessary condition for the existence of a convex realization of a planar linear tree. In the case of broken lines, it is shown that this condition is sufficient; a continuous algorithm constructing such a realization is found.
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N. S. Gusev. Convex Realizations of Planar Linear Trees. Matematičeskie zametki, Tome 73 (2003) no. 5, pp. 665-675. http://geodesic.mathdoc.fr/item/MZM_2003_73_5_a3/

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