Stabbing boxes with finitely many axis-parallel lines and flats
Sutanoya Chakraborty, Arijit Ghosh, Soumi Nandi · Discrete Mathematics · 2024
In this short note, we provide the necessary and sufficient condition for an infinite collection of axis-parallel boxes in R d to be pierceable by finitely many axis-parallel k -flats, where 0 ≤ k < d . We also consider colorful generalizations of the above result and establish their feasibility. The problem considered in this paper is an infinite variant of the Hadwiger-Debrunner ( p , q ) -problem.