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Can anybody give me a hint on how to prove that the straight skeleton of every polygon is a tree. Here is the definition of the straight skeleton (taken from Wikipedia):

The straight skeleton of a polygon is defined by a continuous shrinking process in which the edges of the polygon are moved inwards parallel to themselves at a constant speed. As the edges move in this way, the vertices where pairs of edges meet also move, at speeds that depend on the angle of the vertex. If one of these moving vertices collides with a nonadjacent edge, the polygon is split in two by the collision, and the process continues in each part. The straight skeleton is the set of curves traced out by the moving vertices in this process. In the illustration the top figure shows the shrinking process and the middle figure depicts the straight skeleton in blue.

Here is an example:

Straight skeleton shown in dashed lines.

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I recommend providing definitions of the objects in question; especially that of a 'straight skeleton'. –  Quinn Culver Feb 11 '13 at 16:33
    
@QuinnCulver Would that do? –  staame Feb 11 '13 at 16:48
    
There might be something in Oswin Aichholzer and Franz Aurenhammer, Straight skeletons for general polygonal figures in the plane (117–126), which is in Computing and combinatorics, Proceedings of the 2nd Annual International Conference (COCOON '96) held in Hong Kong, June 17–19, 1996, Edited by Jin-Yi Cai and Chak Kuen Wong, Lecture Notes in Computer Science, 1090, Springer-Verlag, Berlin, 1996, or in Aichholzer, O., Alberts, D., Aurenhammer, F., and Gartner, B. (1995), Straight skeletons of simple polygons, in Proc. 4th Internat. Symp. of LIESMARS, pages 114–124, Wuhan, P.R. China. –  Gerry Myerson Feb 12 '13 at 6:00
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