Geodesic
The geometry of inner spanning trees for planar polygons
Izvestiya. Mathematics , Tome 76 (2012) no. 2, pp. 215-244

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We study the geometry of minimal inner spanning trees for planar polygons (that is, spanning trees whose edge-intervals lie in these polygons). We construct analogues of Voronoi diagrams and Delaunay triangulations, prove that every minimal inner spanning tree is a subgraph of an appropriate Delaunay triangulation, and describe the possible structure of the cells of such triangulations.
Keywords: inner spanning tree, planar polygon, Euclidean spanning tree, Voronoi diagram, Steiner ratio, characteristic domain.
Mots-clés : Delaunay triangulation 
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     author = {A. O. Ivanov and A. A. Tuzhilin},
     title = {The geometry of inner spanning trees for planar polygons},
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A. O. Ivanov; A. A. Tuzhilin. The geometry of inner spanning trees for planar polygons. Izvestiya. Mathematics , Tome 76 (2012) no. 2, pp. 215-244. http://geodesic.mathdoc.fr/item/IM2_2012_76_2_a0/