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Topics on line segments and polygons

โœ Scribed by Kiyoshi Hosono; Masatsugu Urabe; Mamoru Watanabe


Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
217 KB
Volume
151
Category
Article
ISSN
0012-365X

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โœฆ Synopsis


Let S be a set of pairwise disjoint line segments in the plane. Consider the figure F (polygon, tree or path) whose every edge goes through endpoints of elements in S as many as possible, where F does not intersect itself and any element of S. We construct some figures under the preceding conditions.


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On illuminating line segments in the pla
โœ Jurek Czyzowicz; Eduardo Rivera-Campo; Jorge Urrutia; Joseph Zaks ๐Ÿ“‚ Article ๐Ÿ“… 1995 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 269 KB

Let F be a family of n convex sets in the plane. A set of light sources S illuminates F if every point on the boundary of each element of F is visible from at least one element in S. We prove that if F is a family of n line segments, n >/11, then [-2n/3 7 light sources are always sufficient to illum