Geodesic
Minimal binary trees with a regular boundary: The case of skeletons with five endpoints
Matematičeskie zametki, Tome 61 (1997) no. 6, pp. 907-921

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Locally minimal binary trees that span the vertices of regular polygons are studied. Their description is given in the dual language, that of diagonal triangulations of polygons. Diagonal triangulations of a special form, called skeletons, are considered. It is shown that planar binary trees dual to skeletons with five endpoints do not occur among locally minimal binary trees that span the vertices of regular polygons. 
@article{MZM_1997_61_6_a10,
     author = {A. A. Tuzhilin},
     title = {Minimal binary trees with a regular boundary: {The} case of skeletons with five endpoints},
     journal = {Matemati\v{c}eskie zametki},
     pages = {907--921},
     publisher = {mathdoc},
     volume = {61},
     number = {6},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1997_61_6_a10/}
}
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A. A. Tuzhilin. Minimal binary trees with a regular boundary: The case of skeletons with five endpoints. Matematičeskie zametki, Tome 61 (1997) no. 6, pp. 907-921. http://geodesic.mathdoc.fr/item/MZM_1997_61_6_a10/