List Colouring Big Graphs On-Line

In this paper, we investigate the problem of graph list colouring in the on-line setting. We provide several results on paintability of graphs in the model introduced by Schauz [13] and Zhu [20]. We prove that the on-line version of Ohba's conjecture is true in the class of planar graphs. We also consider several alternate on-line list colouring models.