13 citations · 23 across the 7 of their papers we have counts for
4 papers · 1 filter
On contact graphs of totally separable domains
Karoly Bezdek, Muhammad A. Khan, Michael Oliwa
Contact graphs have emerged as an important tool in the study of translative packings of convex bodies. The contact number of a packing of translates of a convex body is the number…
The geometry of homothetic covering and illumination
Karoly Bezdek, Muhammad A. Khan
At a first glance, the problem of illuminating the boundary of a convex body by external light sources and the problem of covering a convex body by its smaller positive homothetic…
Contact numbers for sphere packings
Karoly Bezdek, Muhammad A. Khan
In discrete geometry, the contact number of a given finite number of non-overlapping spheres was introduced as a generalization of Newton's kissing number. This notion has not only…
On the covering index of convex bodies
Karoly Bezdek, Muhammad A. Khan
Covering a convex body by its homothets is a classical notion in discrete geometry that has resulted in a number of interesting and long-standing problems. Swanepoel introduced the…