A note on the lower bound of edge guards of polyhedral terrains
Bose et al. [P. Bose et al., Guarding polyhedral terrains, Comput. Geom., Theory Appl. 6 (1997), pp. 173-185.] proved that (4n-4)/13 edge guards are sometimes necessary to guard an n-vertex polyhedral terrain. Subsequently, Kaucic et al. [B. Kaucic, B. Zalik, and F. Novak, On the lower bound of edge guards of polyhedral terrains, Int. J. Comput. Math. 80 (2003), pp. 811-814.] claimed to find an inconsistency in the proof and used Bose et al. 's proof technique to prove a weaker lower bound of (2n-4)/7 edge-guards. They declared that a proof of the original lower bound of (4n-4)/13 remains an open issue. The purpose of this note is simply to point out that the issue is not open and that Bose et al. 's original proof is correct. We present the original proof of (4n-4)/13 at a level of detail to hopefully remove any misunderstanding of the result.
|Keywords||Computational geometry, Edge guards, Graph theory, Planar graphs, Polyhedral terrains|
|Journal||International Journal of Computer Mathematics|
Bose, P. (2009). A note on the lower bound of edge guards of polyhedral terrains. International Journal of Computer Mathematics, 86(4), 577–583. doi:10.1080/00207160701623046