CovDecRND · Cover-decomposition of multiple coverings under conditions involving randomness

Combinatorial geometry is a very active field where most problems have real life applications. The study of multiple coverings was initiated by Davenport and L. Fejes Toth 50 years ago. In 1986 J. Pach published the first papers about decomposability of multiple coverings. It was discovered recently that besides its theoretical interest, this area has important practical applications. Now there is a great activity in this field with several breakthrough results. The goal of this proposal is to study cover-decomposability, polychromatic colorings and related notions for different geometric and abstract families of sets under various additional conditions, especially random perturbations.