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

Abstract EN

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.