Partial list colouring of certain graphs

Jeannette Janssen, Rogers Mathew, Deepak Rajendraprasad
The partial list colouring conjecture due to Albertson, Grossman, and Haas [1] states that for every s-choosable graph G and every assignment of lists of size t, 1 t s, to the vertices of G there is an induced subgraph of G on at least t|V (G)| s vertices which can be properly coloured from these lists. In this paper, we show that the partial list colouring conjecture holds true for certain classes of graphs like claw-free graphs, graphs with chromatic number at least |V (G)|−1 2 , chordless graphs, and series-parallel graphs.