2026-07-22T13:39:09Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:23213 2025-10-02T12:43:14Z ddc:004 open_access

k-Dimensional Transversals for Fat Convex Sets Jung, Attila Pálvölgyi, Dömötör discrete geometry transversals Helly hypergraphs We prove a fractional Helly theorem for k-flats intersecting fat convex sets. A family ℱ of sets is said to be ρ-fat if every set in the family contains a ball and is contained in a ball such that the ratio of the radii of these balls is bounded by ρ. We prove that for every dimension d and positive reals ρ and α there exists a positive β = β(d,ρ, α) such that if ℱ is a finite family of ρ-fat convex sets in ℝ^d and an α-fraction of the (k+2)-size subfamilies from ℱ can be hit by a k-flat, then there is a k-flat that intersects at least a β-fraction of the sets of ℱ. We prove spherical and colorful variants of the above results and prove a (p,k+2)-theorem for k-flats intersecting balls. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Attila Jung and Dömötör Pálvölgyi 2025 Is Part Of LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SoCG.2025.61 urn:nbn:de:0030-drops-232136 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.61 eng https://creativecommons.org/licenses/by/4.0/legalcode