Abstract :
A graph image is called L-list colourable if there is a vertex colouring of G in which the colour assigned to a vertex image is chosen from a list image associated with this vertex. We say G is image-choosable if all lists image have the cardinality k and G is L-list colourable for all possible assignments of such lists. There are two classical conjectures from Erdős, Rubin and Taylor 1979 about the choosability of planar graphs:
