Abstract
We show that for any set of disjoint line segments in the plane there exists a pointed binary encompassing treeT, that is, a spanning tree on the segment endpoints that contains all input segments, has maximum degree three, and every vertex v ∈ T is pointed, that is, v has an incident angle greater than π. Such a tree can be completed to a minimum pseudo-triangulation. In particular, it follows that every set of disjoint line segments has a minimum pseudo-triangulation of bounded vertex degree.
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Hoffmann, M., Speckmann, B., Tóth, C.D. (2004). Pointed Binary Encompassing Trees. In: Hagerup, T., Katajainen, J. (eds) Algorithm Theory - SWAT 2004. SWAT 2004. Lecture Notes in Computer Science, vol 3111. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27810-8_38
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DOI: https://doi.org/10.1007/978-3-540-27810-8_38
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