Density conditions for panchromatic colourings of hypergraphs (Q1603255)

A panchromatic \(t\)-colouring of a hypergraph \( H =(V,E)\) is a \(t\)-colouring such that each edge has at least one vertex of each colour. Hypergraph \(H\) is panchromatically \(t\)-choosable (panchromatically \(t\)-list-colourable) if, whenever each vertex is given a list of \(t\) colours, the vertices can be panchromatically \(t\)-coloured by using colours from their lists. The number of conditions (depending on the Hall ratio) of a hypergraph to be panchromatically \(t\)-choosable and \(t\)-colourable are given.