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A (k,t)-list assignment L of a graph G is a mapping which assigns a set of size k to each vertex v of G and |⋃v∈V(G)L(v)|=t. A graph G is (k,t)-choosable if G has a proper coloring f such that f(v)∈L(v) for each (k,t)-list assignment L. In 2011, Charoenpanitseri et al. gave a characterization of (k,t)-choosability of n-vertex graphs when t≥kn-k2-2k+1 and left open problems when t≤kn-k2-2k. Recently, Ruksasakchai and Nakprasit obtain the results when t=kn-k2-2k. In this paper, we extend the results to case t=kn-k2-2k-1.

On (k,kn-k2-2k-1)-Choosability of n-Vertex Graphs