Bounds For Partial List Colourings

Let G be a simple graph on n vertices with list chromatic number χl = s. If each vertex of G is assigned a list of t colours Albertson, Grossman and Haas [1] asked how many of the vertices, λ t,s, are necessarily colourable from these lists? They conjectured that λ t,s ≥ tn/s. Their work was extended by Chappell [2]. We improve the known lower bounds for λ t,s. Primary AMS subject classification: 05C15