On a colorful problem by Dol'nikov concerning translates of convex bodies

Leonardo Martínez-Sandoval, Edgardo Roldán-Pensado

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Article number113789
JournalDiscrete Mathematics
Volume347
Issue number3
DOIs
StatePublished - 1 Mar 2024
Externally publishedYes

Keywords

  • Banach-Mazur metric
  • Colorful theorems
  • Piercing number

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

Fingerprint

Dive into the research topics of 'On a colorful problem by Dol'nikov concerning translates of convex bodies'. Together they form a unique fingerprint.

Cite this