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Izvestiya: Mathematics, 2012, Volume 76, Issue 2, Pages 215–244
DOI: https://doi.org/10.1070/IM2012v076n02ABEH002581 (Mi im6595) 		 
The geometry of inner spanning trees for planar polygons

A. O. Ivanovab, A. A. Tuzhilinab

a P. G. Demidov Yaroslavl State University
b M. V. Lomonosov Moscow State University
English version PDF (374 kB) Russian version article
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DOI: https://doi.org/10.1070/IM2012v076n02ABEH002581
Abstract: 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, Delaunay triangulation, Steiner ratio, characteristic domain.
Received: 28.12.2010
Revised: 08.08.2011
Bibliographic databases:
Document Type: Article
UDC: 514.77+512.816.4+517.924.8
MSC: 05C05, 05C35, 51M16, 52B05, 68R10
Language: English
Original paper language: Russian
Citation: A. O. Ivanov, A. A. Tuzhilin, “The geometry of inner spanning trees for planar polygons”, Izv. Math., 76:2 (2012), 215–244
Citation in format AMSBIB
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\paper The geometry of inner spanning trees for planar polygons
\jour Izv. Math.
\yr 2012
\vol 76
\issue 2
\pages 215--244
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