Abstract
In this note we study a conjecture by Jerónimo-Castro, Magazinov and Soberón which generalized a question posed by Dol'nikov. Let F1,F2,…,Fn be families of translates of a convex compact set K in the plane so that each two sets from distinct families intersect. We show that, for some j, ⋃i≠jFi can be pierced by at most 4 points. To do so, we use previous ideas from Gomez-Navarro and Roldán-Pensado together with an approximation result closely tied to the Banach-Mazur distance to the square.
Original language | English |
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Article number | 113789 |
Journal | Discrete Mathematics |
Volume | 347 |
Issue number | 3 |
DOIs | |
State | Published - 1 Mar 2024 |
Externally published | Yes |
Keywords
- Banach-Mazur metric
- Colorful theorems
- Piercing number
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics