Some New Results on Geometric Transversals - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Discrete and Computational Geometry Année : 2023

Some New Results on Geometric Transversals

Résumé

We investigate a number of questions, problems, and conjectures related to geometric transversal theory. Among our results we disprove a conjecture of Bárány and Kalai regarding weak ε-nets for k-flats and convex sets in Rd , and we prove a conjecture of Arocha, Bracho, and Montejano regarding a colorful version of the Goodman–Pollack–Wenger transversal theorem. We also investigate the connected components of the space of line transversals to pairwise disjoint convex sets in R3 , and we extend a theorem of Karasev and Montejano regarding colorful intersections and k-transversals.
Fichier non déposé

Dates et versions

hal-04293155 , version 1 (18-11-2023)

Identifiants

Citer

Otfried Cheong, Xavier Goaoc, Andreas Holmsen. Some New Results on Geometric Transversals. Discrete and Computational Geometry, inPress, ⟨10.1007/s00454-023-00573-2⟩. ⟨hal-04293155⟩
40 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More