Edge guards for polyhedra in three-space

Javier Cano,Csaba D. Tóth,Jorge Urrutia,Giovanni Viglietta

Computational Geometry（2022）

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摘要

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 of the polyhedron is disconnected (i.e., if the polyhedron has “holes”), and regardless of the genus of each connected component of its boundary.

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关键词

Art Gallery Problem,Edge guard,Polyhedron,Edge cover,1-skeleton

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