A note on a list colouring of hypergraphs

Abstract. In the note we present two results. The first of them gives a sufficient condition for a colouring of a hypergraph from an assigned list. It generalises the analogous fact for graphs. The second result states that for every \(k\geq 3\) and every \(l\geq 2\), a distance between the list chromatic number and the chromatic number can be arbitrarily large in the class of \(k\)-uniform hypergraphs with the chromatic number bounded below by \(l\). A similar result for \(k\)-uniform, \(2\)-colorable hypergraphs is known but the proof techniques are different.