Edge guards for polyhedra in three-space
نویسندگان
چکیده
It is shown that every polyhedron in R3 can be guarded by at most 56 of its edges. This result holds even if the boundary disconnected (i.e., has “holes”), and regardless genus each connected component boundary. When a homeomorphic to ball all faces are triangles, bound improved slightly 2936
منابع مشابه
Edge Guards for Polyhedra in Three-Space
It is shown that every polyhedron in R3 with m edges can be guarded with at most 27 32m edge guards. The bound improves to 6m + 1 12 if the 1-skeleton of the polyhedron is connected. These are the first non-trivial upper bounds for the edge guard problem for general polyhedra in R3.
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ژورنال
عنوان ژورنال: Computational Geometry: Theory and Applications
سال: 2022
ISSN: ['0925-7721', '1879-081X']
DOI: https://doi.org/10.1016/j.comgeo.2022.101859