Stabbing boxes with finitely many axis-parallel lines and flats
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.
Authors
- Arijit Ghosh (ORCID: https://orcid.org/0000-0001-9400-9863)
- Soumi Nandi (ORCID: https://orcid.org/0009-0006-3119-7768)
- Sutanoya Chakraborty
Institutions
- Indian Statistical Institute (IN)
Publication Details
- Journal
- Discrete Mathematics
- Published
- 2024-09-26
- DOI
- https://doi.org/10.1016/j.disc.2024.114269
- Citations
- 1
- Primary Topic
- Computational Geometry and Mesh Generation
- Type
- article
- Field-Weighted Citation Impact
- 0.63
Funders
- Department of Science and Technology, Ministry of Science and Technology, India
- Science and Engineering Research Board