Opuscula Math.
24
, no. 2
(), 171-175
Opuscula Mathematica

# 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.
Keywords: hypergraph, list colouring.
Mathematics Subject Classification: 05C65, 05C15.