Geodesic
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. 
@article{MZM_2003_73_5_a3,
     author = {N. S. Gusev},
     title = {Convex {Realizations} of {Planar} {Linear} {Trees}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {665--675},
     publisher = {mathdoc},
     volume = {73},
     number = {5},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2003_73_5_a3/}
}
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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/