Partial List Colouring of Certain Graphs

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 6 t 6 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. ∗While this work was done, the author was an AARMS postdoctoral fellow in the Department of Mathematics and Statistics, Dalhousie University, Halifax, Canada B3H 3J5. †While this work was done, the author was supported by a VATAT Postdoctoral Fellowship and the Israel Science Foundation (grant number 862/10). the electronic journal of combinatorics 22(3) (2015), #P3.41 1